<html><head><meta http-equiv="Content-Type" content="text/html; charset=utf-8"></head><body style="word-wrap: break-word; -webkit-nbsp-mode: space; line-break: after-white-space;" class="">皆様、<div class=""><br class=""></div><div class="">大阪大学の糟谷です。</div><div class="">大阪大学の幾何学セミナーの予定にについて下記におしらせします。</div><div class=""><br class=""></div><div class=""><br class=""></div><div class=""><center style="font-family: -webkit-standard;" class=""><span style="font-size: medium;" class="">11/30(Mon) </span><span style="font-size: medium;" class="">13:00--14:30 </span>濱中翔太（中央大学）</center><br style="font-family: -webkit-standard;" class=""><center style="font-family: -webkit-standard;" class="">Decompositions of the space of Riemannian metrics on a compact manifold with boundary</center><p style="font-family: -webkit-standard;" class="">In this talk, I will show some decomposition theorems for the space of all Riemannian metrics on a compact manifold with boundary endowed with a fixed conformal class on the boundary. These are extensions of Koiso’s decomposition theorem and Ebin’s slice theorem to a manifold with boundary, respectively. I will also explain applications to a rigidity theorem of relative constant scalar curvature metrics and a characterization of relative Einstein metrics. </p></div><div class=""><br class=""></div><div class=""><br class=""></div><div class=""><center style="font-family: -webkit-standard;" class=""><span style="font-size: medium;" class="">12/7(Mon) </span><span style="font-size: medium;" class="">13:00--14:30 </span>岩井雅崇(大阪市大、RIMS)</center><br style="font-family: -webkit-standard;" class=""><center style="font-family: -webkit-standard;" class="">正則接ベクトル束が正値性を持つ部分束を含むときの代数多様体の構造について</center><p style="font-family: -webkit-standard;" class="">射影代数多様体Xの正則接ベクトル束<span id="MathJax-Element-1-Frame" class="MathJax_CHTML mjx-chtml" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>T</mi><mi>X</mi></msub></math>" role="presentation" style="display: inline-block; line-height: 0; font-size: 19.360000610351563px; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;"><span id="MJXc-Node-1" class="mjx-math" aria-hidden="true" style="display: inline-block; border-collapse: separate; border-spacing: 0px;"><span id="MJXc-Node-2" class="mjx-mrow" style="display: inline-block; box-sizing: content-box !important;"><span id="MJXc-Node-3" class="mjx-msubsup" style="display: inline-block; box-sizing: content-box !important;"><span class="mjx-base" style="display: inline-block; margin-right: -0.12em; box-sizing: content-box !important;"><span id="MJXc-Node-4" class="mjx-mi" style="display: inline-block; box-sizing: content-box !important;"><span class="mjx-char MJXc-TeX-math-I" style="display: block; white-space: pre; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; padding-top: 0.467em; padding-bottom: 0.261em; padding-right: 0.12em; box-sizing: content-box !important;">T</span></span></span><span class="mjx-sub" style="display: inline-block; font-size: 13.687519073486328px; vertical-align: -0.212em; padding-right: 0.071em; box-sizing: content-box !important;"><span id="MJXc-Node-5" class="mjx-mi" style="display: inline-block; box-sizing: content-box !important;"><span class="mjx-char MJXc-TeX-math-I" style="display: block; white-space: pre; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; padding-top: 0.467em; padding-bottom: 0.261em; padding-right: 0.024em; box-sizing: content-box !important;">X</span></span></span></span></span></span><span class="MJX_Assistive_MathML" role="presentation" style="top: 0px; left: 0px; clip: rect(1px, 1px, 1px, 1px); -webkit-user-select: none; position: absolute !important; padding: 1px 0px 0px !important; border: 0px !important; height: 1px !important; width: 1px !important; overflow: hidden !important; display: block !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>T</mi><mi>X</mi></msub></math></span></span>が正値性を持つとき, Xの構造は限定 されることがわかっている. 例えば, 森から「<span id="MathJax-Element-2-Frame" class="MathJax_CHTML mjx-chtml" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>T</mi><mi>X</mi></msub></math>" role="presentation" style="display: inline-block; line-height: 0; font-size: 19.360000610351563px; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;"><span id="MJXc-Node-6" class="mjx-math" aria-hidden="true" style="display: inline-block; border-collapse: separate; border-spacing: 0px;"><span id="MJXc-Node-7" class="mjx-mrow" style="display: inline-block; box-sizing: content-box !important;"><span id="MJXc-Node-8" class="mjx-msubsup" style="display: inline-block; box-sizing: content-box !important;"><span class="mjx-base" style="display: inline-block; margin-right: -0.12em; box-sizing: content-box !important;"><span id="MJXc-Node-9" class="mjx-mi" style="display: inline-block; box-sizing: content-box !important;"><span class="mjx-char MJXc-TeX-math-I" style="display: block; white-space: pre; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; padding-top: 0.467em; padding-bottom: 0.261em; padding-right: 0.12em; box-sizing: content-box !important;">T</span></span></span><span class="mjx-sub" style="display: inline-block; font-size: 13.687519073486328px; vertical-align: -0.212em; padding-right: 0.071em; box-sizing: content-box !important;"><span id="MJXc-Node-10" class="mjx-mi" style="display: inline-block; box-sizing: content-box !important;"><span class="mjx-char MJXc-TeX-math-I" style="display: block; white-space: pre; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; padding-top: 0.467em; padding-bottom: 0.261em; padding-right: 0.024em; box-sizing: content-box !important;">X</span></span></span></span></span></span><span class="MJX_Assistive_MathML" role="presentation" style="top: 0px; left: 0px; clip: rect(1px, 1px, 1px, 1px); -webkit-user-select: none; position: absolute !important; padding: 1px 0px 0px !important; border: 0px !important; height: 1px !important; width: 1px !important; overflow: hidden !important; display: block !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>T</mi><mi>X</mi></msub></math></span></span>が豊富ならば, Xは複素射影 空間<span id="MathJax-Element-3-Frame" class="MathJax_CHTML mjx-chtml" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">C</mi><mi mathvariant="double-struck">P</mi></mrow><mi>n</mi></msup></math>" role="presentation" style="display: inline-block; line-height: 0; font-size: 19.360000610351563px; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;"><span id="MJXc-Node-11" class="mjx-math" aria-hidden="true" style="display: inline-block; border-collapse: separate; border-spacing: 0px;"><span id="MJXc-Node-12" class="mjx-mrow" style="display: inline-block; box-sizing: content-box !important;"><span id="MJXc-Node-13" class="mjx-msubsup" style="display: inline-block; box-sizing: content-box !important;"><span class="mjx-base" style="display: inline-block; box-sizing: content-box !important;"><span id="MJXc-Node-14" class="mjx-texatom" style="display: inline-block; box-sizing: content-box !important;"><span id="MJXc-Node-15" class="mjx-mrow" style="display: inline-block; box-sizing: content-box !important;"><span id="MJXc-Node-16" class="mjx-mi" style="display: inline-block; box-sizing: content-box !important;"><span class="mjx-char MJXc-TeX-ams-R" style="display: block; white-space: pre; font-family: MJXc-TeX-ams-R, MJXc-TeX-ams-Rw; padding-top: 0.467em; padding-bottom: 0.313em; box-sizing: content-box !important;">C</span></span><span id="MJXc-Node-17" class="mjx-mi" style="display: inline-block; box-sizing: content-box !important;"><span class="mjx-char MJXc-TeX-ams-R" style="display: block; white-space: pre; font-family: MJXc-TeX-ams-R, MJXc-TeX-ams-Rw; padding-top: 0.416em; padding-bottom: 0.313em; box-sizing: content-box !important;">P</span></span></span></span></span><span class="mjx-sup" style="display: inline-block; font-size: 13.687519073486328px; vertical-align: 0.642em; padding-left: 0px; padding-right: 0.071em; box-sizing: content-box !important;"><span id="MJXc-Node-18" class="mjx-mi" style="display: inline-block; box-sizing: content-box !important;"><span class="mjx-char MJXc-TeX-math-I" style="display: block; white-space: pre; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; padding-top: 0.209em; padding-bottom: 0.313em; box-sizing: content-box !important;">n</span></span></span></span></span></span><span class="MJX_Assistive_MathML" role="presentation" style="top: 0px; left: 0px; clip: rect(1px, 1px, 1px, 1px); -webkit-user-select: none; position: absolute !important; padding: 1px 0px 0px !important; border: 0px !important; height: 1px !important; width: 1px !important; overflow: hidden !important; display: block !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mrow class="MJX-TeXAtom-ORD"><mi mathvariant="double-struck">C</mi><mi mathvariant="double-struck">P</mi></mrow><mi>n</mi></msup></math></span></span>と同型である」ことが知られており, Campana-Peternellと Demailly-Peternell-Schneiderから「<span id="MathJax-Element-4-Frame" class="MathJax_CHTML mjx-chtml" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>T</mi><mi>X</mi></msub></math>" role="presentation" style="display: inline-block; line-height: 0; font-size: 19.360000610351563px; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;"><span id="MJXc-Node-19" class="mjx-math" aria-hidden="true" style="display: inline-block; border-collapse: separate; border-spacing: 0px;"><span id="MJXc-Node-20" class="mjx-mrow" style="display: inline-block; box-sizing: content-box !important;"><span id="MJXc-Node-21" class="mjx-msubsup" style="display: inline-block; box-sizing: content-box !important;"><span class="mjx-base" style="display: inline-block; margin-right: -0.12em; box-sizing: content-box !important;"><span id="MJXc-Node-22" class="mjx-mi" style="display: inline-block; box-sizing: content-box !important;"><span class="mjx-char MJXc-TeX-math-I" style="display: block; white-space: pre; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; padding-top: 0.467em; padding-bottom: 0.261em; padding-right: 0.12em; box-sizing: content-box !important;">T</span></span></span><span class="mjx-sub" style="display: inline-block; font-size: 13.687519073486328px; vertical-align: -0.212em; padding-right: 0.071em; box-sizing: content-box !important;"><span id="MJXc-Node-23" class="mjx-mi" style="display: inline-block; box-sizing: content-box !important;"><span class="mjx-char MJXc-TeX-math-I" style="display: block; white-space: pre; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; padding-top: 0.467em; padding-bottom: 0.261em; padding-right: 0.024em; box-sizing: content-box !important;">X</span></span></span></span></span></span><span class="MJX_Assistive_MathML" role="presentation" style="top: 0px; left: 0px; clip: rect(1px, 1px, 1px, 1px); -webkit-user-select: none; position: absolute !important; padding: 1px 0px 0px !important; border: 0px !important; height: 1px !important; width: 1px !important; overflow: hidden !important; display: block !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>T</mi><mi>X</mi></msub></math></span></span>がネフならば, XはFano多様体とAbel 多様体で構成される」ことが知られている. これらの結果は<span id="MathJax-Element-5-Frame" class="MathJax_CHTML mjx-chtml" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>T</mi><mi>X</mi></msub></math>" role="presentation" style="display: inline-block; line-height: 0; font-size: 19.360000610351563px; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;"><span id="MJXc-Node-24" class="mjx-math" aria-hidden="true" style="display: inline-block; border-collapse: separate; border-spacing: 0px;"><span id="MJXc-Node-25" class="mjx-mrow" style="display: inline-block; box-sizing: content-box !important;"><span id="MJXc-Node-26" class="mjx-msubsup" style="display: inline-block; box-sizing: content-box !important;"><span class="mjx-base" style="display: inline-block; margin-right: -0.12em; box-sizing: content-box !important;"><span id="MJXc-Node-27" class="mjx-mi" style="display: inline-block; box-sizing: content-box !important;"><span class="mjx-char MJXc-TeX-math-I" style="display: block; white-space: pre; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; padding-top: 0.467em; padding-bottom: 0.261em; padding-right: 0.12em; box-sizing: content-box !important;">T</span></span></span><span class="mjx-sub" style="display: inline-block; font-size: 13.687519073486328px; vertical-align: -0.212em; padding-right: 0.071em; box-sizing: content-box !important;"><span id="MJXc-Node-28" class="mjx-mi" style="display: inline-block; box-sizing: content-box !important;"><span class="mjx-char MJXc-TeX-math-I" style="display: block; white-space: pre; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; padding-top: 0.467em; padding-bottom: 0.261em; padding-right: 0.024em; box-sizing: content-box !important;">X</span></span></span></span></span></span><span class="MJX_Assistive_MathML" role="presentation" style="top: 0px; left: 0px; clip: rect(1px, 1px, 1px, 1px); -webkit-user-select: none; position: absolute !important; padding: 1px 0px 0px !important; border: 0px !important; height: 1px !important; width: 1px !important; overflow: hidden !important; display: block !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>T</mi><mi>X</mi></msub></math></span></span>が巨大や擬有 効のときでも拡張できることがわかっている. 一方でPeternellは「<span id="MathJax-Element-6-Frame" class="MathJax_CHTML mjx-chtml" tabindex="0" data-mathml="<math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>T</mi><mi>X</mi></msub></math>" role="presentation" style="display: inline-block; line-height: 0; font-size: 19.360000610351563px; word-wrap: normal; word-spacing: normal; white-space: nowrap; float: none; direction: ltr; max-width: none; max-height: none; min-width: 0px; min-height: 0px; border: 0px; margin: 0px; padding: 1px 0px; position: relative;"><span id="MJXc-Node-29" class="mjx-math" aria-hidden="true" style="display: inline-block; border-collapse: separate; border-spacing: 0px;"><span id="MJXc-Node-30" class="mjx-mrow" style="display: inline-block; box-sizing: content-box !important;"><span id="MJXc-Node-31" class="mjx-msubsup" style="display: inline-block; box-sizing: content-box !important;"><span class="mjx-base" style="display: inline-block; margin-right: -0.12em; box-sizing: content-box !important;"><span id="MJXc-Node-32" class="mjx-mi" style="display: inline-block; box-sizing: content-box !important;"><span class="mjx-char MJXc-TeX-math-I" style="display: block; white-space: pre; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; padding-top: 0.467em; padding-bottom: 0.261em; padding-right: 0.12em; box-sizing: content-box !important;">T</span></span></span><span class="mjx-sub" style="display: inline-block; font-size: 13.687519073486328px; vertical-align: -0.212em; padding-right: 0.071em; box-sizing: content-box !important;"><span id="MJXc-Node-33" class="mjx-mi" style="display: inline-block; box-sizing: content-box !important;"><span class="mjx-char MJXc-TeX-math-I" style="display: block; white-space: pre; font-family: MJXc-TeX-math-I, MJXc-TeX-math-Ix, MJXc-TeX-math-Iw; padding-top: 0.467em; padding-bottom: 0.261em; padding-right: 0.024em; box-sizing: content-box !important;">X</span></span></span></span></span></span><span class="MJX_Assistive_MathML" role="presentation" style="top: 0px; left: 0px; clip: rect(1px, 1px, 1px, 1px); -webkit-user-select: none; position: absolute !important; padding: 1px 0px 0px !important; border: 0px !important; height: 1px !important; width: 1px !important; overflow: hidden !important; display: block !important;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>T</mi><mi>X</mi></msub></math></span></span>の部分束Fが正値性を持つときも, Xの構造は限られ るであろう」と予想した. この講演ではPeternellの問題について, 関連研究や 講演者によって得られた結果を紹介する.</p><p style="font-family: -webkit-standard;" class=""><br class=""></p><p style="font-family: -webkit-standard;" class=""> ----------------- 対面でのセミナーです。 聴講者は手指の消毒、マスク着用、ソーシャルディスタンス等感染症への対策にご協力いただくようお願いします。ご協力いただけない場合はご退室をお願いする場合があります。また感染症への対策のため入室人数を制限する場合があります。特に講演開始後の入室ができなくなる場合があります。セミナー室に来られない聴講希望者のためにオンラインでのセミナー映像のリアルタイム配信を企画しております。希望者は以下のフォームに登録お願いします。<a href="https://docs.google.com/forms/d/1QZr7GchFF8xlElZd-0k2XTBKm5V6_tStFcjku-p30Pg/edit" class="">https://docs.google.com/forms/d/1QZr7GchFF8xlElZd-0k2XTBKm5V6_tStFcjku-p30Pg/edit</a> </p></div><div class=""><br class=""></div><div class="">よろしくお願いします。</div></body></html>