Text only print
Full screen print
Geometry Colloquium
Seminar information archive ～06/13｜Next seminar｜Future seminars 06/14～
| Date, time & place | Friday 10:00 - 11:30 126Room #126 (Graduate School of Math. Sci. Bldg.) |
|---|
2013/01/30
10:30-12:00 Room #128 (Graduate School of Math. Sci. Bldg.)
Ryoichi Kobayashi (Nagoya University)
Hamiltonian Volume Minimizing Property of Maximal Torus Orbits in the Complex Projective Space (JAPANESE)
Ryoichi Kobayashi (Nagoya University)
Hamiltonian Volume Minimizing Property of Maximal Torus Orbits in the Complex Projective Space (JAPANESE)
[ Abstract ]
We prove that any U(1)n-orbit in BbbPn 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 TttinDeltan and consider its Hamiltonian deformation phi(Tt)tinDeltan where phi is a Hamiltobian diffeomorphism of BbbPn,
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 H0(BbbPn,CalO(k)) obtained by semi-classical approximation of the CalO(k) Bohr-Sommerfeld tori of the Lagrangian torus fibration TttinDeltan and its Hamiltonian deformation phi(Tt)tinDeltan.
We prove that any U(1)n-orbit in BbbPn 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 TttinDeltan and consider its Hamiltonian deformation phi(Tt)tinDeltan where phi is a Hamiltobian diffeomorphism of BbbPn,
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 H0(BbbPn,CalO(k)) obtained by semi-classical approximation of the CalO(k) Bohr-Sommerfeld tori of the Lagrangian torus fibration TttinDeltan and its Hamiltonian deformation phi(Tt)tinDeltan.
