複素解析幾何セミナー

過去の記録 ~01/27次回の予定今後の予定 01/28~

開催情報 月曜日 10:30~12:00 数理科学研究科棟(駒場) 128号室
担当者 平地 健吾, 高山 茂晴, 野村 亮介

2022年10月31日(月)

10:30-12:00   数理科学研究科棟(駒場) 128号室
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井上 瑛二 氏 (理化学研究所)
The non-archimedean μ-entropy in toric case (Japanese)
[ 講演概要 ]
The non-archimedean μ-entropy is a functional on the space of test configurations of a polarized variety. It plays a key role in μK-stability and can be interpreted as a dual functional to Perelman’s μ-entropy for Kahler metrics. The fundamental question on the non-archimedean μ-entropy is the existence and uniqueness of maximizers. To find its maximizers, it is natural to extend the functional to a suitable completion of the space of test configurations. For general polarized variety, we can realize such completion and extension based on the non-archimedean pluripotential theory.
In the toric case, the torus invariant subspace of the completion is identified with a suitable space of convex functions on the moment polytope and then the non-archimedean μ-entropy is simply expressed by integrations of convex functions on the polytope. I will show a compactness result in the toric case, by which we conclude the existence of maximizers for the toric non-archimedean μ-entropy.
[ 参考URL ]
https://forms.gle/hYT2hVhDE3q1wDSh6