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Seminar on Geometric Complex Analysis
Seminar information archive ～04/25｜Next seminar｜Future seminars 04/26～
| Date, time & place | Monday 10:30 - 12:00 128Room #128 (Graduate School of Math. Sci. Bldg.) |
|---|---|
| Organizer(s) | Kengo Hirachi, Shigeharu Takayama |
2022/05/30
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Yusaku Tiba (Ochanomizu University)
Asymptotic estimates of holomorphic sections on Bohr-Sommerfeld Lagrangian submanifolds (Japanese)
https://forms.gle/hYT2hVhDE3q1wDSh6
Yusaku Tiba (Ochanomizu University)
Asymptotic estimates of holomorphic sections on Bohr-Sommerfeld Lagrangian submanifolds (Japanese)
[ Abstract ]
In this talk, we study an asymptotic estimate of holomorphic sections of a positive line bundle. Let $M$ be a complex manifold and $L$ be a positive line bundle over $M$ with a Hermitian metric $h$ whose Chern form is a Kähler form $\omega$. Let $X \subset M$ be a Lagrangian submanifold of $(M, \omega)$. When $X$ satisfies the Bohr-Sommerfeld condition, we prove a submean value theorem for holomorphic sections and we give an asymptotic estimate of $\inf_{x \in X}|f(x)|_{h^k}$ for $f \in H^0(M, L^k)$. This estimate provides an analog result about the leading term of the asymptotic series expansion formula of the Bergman kernel function.
[ Reference URL ]In this talk, we study an asymptotic estimate of holomorphic sections of a positive line bundle. Let $M$ be a complex manifold and $L$ be a positive line bundle over $M$ with a Hermitian metric $h$ whose Chern form is a Kähler form $\omega$. Let $X \subset M$ be a Lagrangian submanifold of $(M, \omega)$. When $X$ satisfies the Bohr-Sommerfeld condition, we prove a submean value theorem for holomorphic sections and we give an asymptotic estimate of $\inf_{x \in X}|f(x)|_{h^k}$ for $f \in H^0(M, L^k)$. This estimate provides an analog result about the leading term of the asymptotic series expansion formula of the Bergman kernel function.
https://forms.gle/hYT2hVhDE3q1wDSh6
