题目：Some Applications of Symplectic Reduction to Complex Analysis and Geometry
报告人: Daniel Burns University of Michigan,US
时 间: 5月19日 星期一 下午4:00 -5:30
地 点: 管理科研楼1611会议室
摘 要: We review the problem of algebraicizing a closed analytic submanifold $X /subset C^N$. One formulation of this is to find very slowly growing entire functions on $X$ which serve to give a polynomial embedding of $X$ into another $C^{N_1}$. To measure slowness, we use plurisubharmonic solutions $u$ of the homogeneous complex Monge-Ampere equation (HCMA) $(/partial/bar/partial u)^n = 0$. The polynomial growth condition on an entire holomorphic function $f$ will be $|f| /le C(1 + /tau)^{N'}$, where $/tau:= e^u$, and $N' /in N^+$, for some positive integer $N'$ which depends on $f$. A class of complex manifolds with such HCMA exhaustions is given by entire Grauert tubes, manifolds which are complex structures placed on the tangent bundle of a Riemannian manifold $M$. Aguilar has shown a construction via symplectic reduction of all known examples of such entire tubes. His work shows they come in continuous biholomorphic families. In joint work we show that these entire tubes are affine algebraic varieties, and if they are biholomorphic, they are isomorphic as algebraic varieties. This is joint work with Zhou Zhang (University of Sydney), and relies on earlier work of the speaker with Victor Guillemin and Zuoqin Wang on stability functions in symplectic reduction.
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