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| 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 |
2020年07月13日(月)
10:30-12:00 オンライン開催
井上瑛二 氏 (東大数理)
$\mu$-cscK metrics and $\mu$K-stability of polarized manifolds
https://forms.gle/vSFPoVR6ugrkTGhX7
井上瑛二 氏 (東大数理)
$\mu$-cscK metrics and $\mu$K-stability of polarized manifolds
[ 講演概要 ]
I firstly talk about some backgrounds on the following two frameworks; "cscK metrics & K-stability" and "Kähler-Ricci soliton & modified K-stability", whose intersection is precisely the framework on "Kähler-Einstein metrics & K-stability".
I will introduce a new framework unifying these frameworks, which I call the framework on "$\mu$-cscK metrics and $\mu$K-stability".
There are two divided contents:
1. I explain formulation and first motivation for $\mu$-cscK metrics and give brief remarks on results parallel to those for cscK metrics / Kähler-Ricci solitons. I will illustrate some attractive features/phenomenon special to $\mu$-cscK metrics by examples; "extremal limit" and "phase transition".
(cf. https://arxiv.org/abs/1902.00664)
2. I explain how one should/can formulate/derive/express $\mu$-Futaki invariant of test configurations with general singularities. We also construct a characteristic class for families of polarized schemes, which generalizes the CM line bundle in K-stability. I also give a few words on applications to moduli problem.
(cf. https://arxiv.org/abs/2004.06393)
[ 参考URL ]I firstly talk about some backgrounds on the following two frameworks; "cscK metrics & K-stability" and "Kähler-Ricci soliton & modified K-stability", whose intersection is precisely the framework on "Kähler-Einstein metrics & K-stability".
I will introduce a new framework unifying these frameworks, which I call the framework on "$\mu$-cscK metrics and $\mu$K-stability".
There are two divided contents:
1. I explain formulation and first motivation for $\mu$-cscK metrics and give brief remarks on results parallel to those for cscK metrics / Kähler-Ricci solitons. I will illustrate some attractive features/phenomenon special to $\mu$-cscK metrics by examples; "extremal limit" and "phase transition".
(cf. https://arxiv.org/abs/1902.00664)
2. I explain how one should/can formulate/derive/express $\mu$-Futaki invariant of test configurations with general singularities. We also construct a characteristic class for families of polarized schemes, which generalizes the CM line bundle in K-stability. I also give a few words on applications to moduli problem.
(cf. https://arxiv.org/abs/2004.06393)
https://forms.gle/vSFPoVR6ugrkTGhX7
