[geometry-ml:04068] Geometric Complex Analysis Seminar 6/8

[Kengo Hirachi]

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2020年6月8日(月) 10:30-12:00   Zoom 開催
橋本義規 氏 (東京工業大学)
Applications of the Quot-scheme limit to variational aspects of the Hermitian-Einstein metric

[ 講演概要 ]
The Kobayashi-Hitchin correspondence, proved by Donaldson and Uhlenbeck-Yau by using the nonlinear PDE theory, states that the existence of Hermitian-Einstein metrics on a holomorphic vector bundle is equivalent to an algebro-geometric stability condition. We present some results that exhibit an explicit link between differential and algebraic geometry in the above correspondence, from a variational point of view. The key to such results is an object called the Quot-scheme limit of Fubini-Study metrics, which is used to evaluate certain algebraic 1-parameter subgroups of Hermitian metrics by using the theory of Quot-schemes in algebraic geometry. This method also works for the proof of the correspondence between the balanced metrics and the Gieseker stability, as originally proved by X.W. Wang. Joint work with Julien Keller.

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平地 健吾, 高山 茂晴