[geometry-ml:01392] Seminar at IPMU on 1/19, 1/20 Verbitsky

[Satoshi Kondo]

Dear colleagues:

We announce the following two talks at IPMU
(the Institute for the Physics and Mathematics of the Universe).

Regards,

Satoshi Kondo (IPMU)
http://ipmu.jp/

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Speaker: Misha Verbitsky (IPMU)

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Date: Jan 19 (Thu) 15:30-17:00

Place: Seminar room A

Title: Trisymplectic manifolds

Abstract:
A trisymplectic structure on a complex 2n-manifold is a
triple of holomorphic symplectic forms such that any
linear combination of these forms has rank 2n, n or 0. We
show that a trisymplectic manifold is equipped with a
holomorphic 3-web and the Chern connection of this 3-web
is holomorphic, torsion-free, and preserves the three
symplectic forms. We construct a trisymplectic structure
on the moduli of regular rational curves in the twistor
space of a hyperkaehler manifold. We show that the moduli
space $M$ of holomorphic vector bundles on $CP^3$ that are
trivial along a line admits a trisymplectic structure.
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Date: Jan 20 (Fri) 10:30-12:30

Place: Seminar room A

Title: Global Torelli theorem for hyperkahler manifolds"

Abstract:
A mapping class group of an oriented manifold is a
quotient of its diffeomorphism group by the isotopies. We
compute a mapping class group of a hypekahler manifold
$M$, showing that it is commensurable to an arithmetic
subgroup in SO(3, b_2-3). A Teichmuller space of $M$ is a
space of complex structures on $M$ up to isotopies. We
define a birational Teichmuller space by identifying
certain points corresponding to bimeromorphically
equivalent manifolds, and show that the period map gives
an isomorphism of the birational Teichmuller space and the
corresponding period space $SO(b_2-3, 3)/SO(2)\times
SO(b_2 -3, 1)$. We use this result to obtain a Torelli
theorem identifying any connected component of birational
moduli space with a quotient of a period space by an
arithmetic subgroup. When $M$ is a Hilbert scheme of $n$
points on a K3 surface, with $n-1$ a prime power, our
Torelli theorem implies the usual Hodge-theoretic
birational Torelli theorem (for other examples of
hyperkahler manifolds the Hodge-theoretic Torelli theorem
is known to be false). This also proves the Torelli
theorem for K3 surfaces.
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You can check the location from
http://www.ipmu.jp/access-0
The schedule of the seminar can be checked from
http://db.ipmu.jp/seminar/