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| 開催情報 | 金曜日 10:00～11:30 数理科学研究科棟(駒場) 126号室 |
|---|---|
| 担当者 | 植田一石，金井雅彦，二木昭人 |
| 備考 | 開始時間と開催場所などは変更されることがあるので, セミナーごとにご確認ください. |
2013年01月30日(水)
10:30-12:00 数理科学研究科棟(駒場) 128号室
開始時間と開催場所などは変更されることがあるので, セミナーごとにご確認ください.
小林亮一 氏 (名古屋大学)
Hamiltonian Volume Minimizing Property of Maximal Torus Orbits in the Complex Projective Space (JAPANESE)
開始時間と開催場所などは変更されることがあるので, セミナーごとにご確認ください.
小林亮一 氏 (名古屋大学)
Hamiltonian Volume Minimizing Property of Maximal Torus Orbits in the Complex Projective Space (JAPANESE)
[ 講演概要 ]
We prove that any $U(1)^n$-orbit in $\\Bbb P^n$ is volume minimizing under Hamiltonian deformation.
The idea of the proof is :
- (1) We extend one $U(1)^n$-orbit to the momentum torus fibration $\\{T_t\\}_{t\\in\\Delta^n}$ and consider its Hamiltonian deformation $\\{\\phi(T_t)\\}_{t\\in\\Delta^n}$ where $\\phi$ is a Hamiltobian diffeomorphism of $\\Bbb P^n$,
and then :
- (2) We compare each $U(1)^n$-orbit and its Hamiltonian deformation by compaing the large $k$ asymptotic behavior of the sequence of projective embeddings defined, for each $k$, by the basis of $H^0(\\Bbb P^n,\\Cal O(k))$ obtained by semi-classical approximation of the $\\Cal O(k)$ Bohr-Sommerfeld tori of the Lagrangian torus fibration $\\{T_t\\}_{t\\in\\Delta^n}$ and its Hamiltonian deformation $\\{\\phi(T_t)\\}_{t\\in\\Delta^n}$.
We prove that any $U(1)^n$-orbit in $\\Bbb P^n$ is volume minimizing under Hamiltonian deformation.
The idea of the proof is :
- (1) We extend one $U(1)^n$-orbit to the momentum torus fibration $\\{T_t\\}_{t\\in\\Delta^n}$ and consider its Hamiltonian deformation $\\{\\phi(T_t)\\}_{t\\in\\Delta^n}$ where $\\phi$ is a Hamiltobian diffeomorphism of $\\Bbb P^n$,
and then :
- (2) We compare each $U(1)^n$-orbit and its Hamiltonian deformation by compaing the large $k$ asymptotic behavior of the sequence of projective embeddings defined, for each $k$, by the basis of $H^0(\\Bbb P^n,\\Cal O(k))$ obtained by semi-classical approximation of the $\\Cal O(k)$ Bohr-Sommerfeld tori of the Lagrangian torus fibration $\\{T_t\\}_{t\\in\\Delta^n}$ and its Hamiltonian deformation $\\{\\phi(T_t)\\}_{t\\in\\Delta^n}$.
