Torus Actions and Singularities in Symplectic Geometry.

[摘要] This thesis begins with a generalization of two classic results about toric varieties to the context of varieties with codimension-one torus actions: the toric cone theorem and the intersection formula for invariant curves and divisors. Leaving algebraic toric geometry for symplectic toric geometry, we then prove a Delzant-type classification of torus actions on manifolds equipped with symplectic structures that have mild order-one singularities (called b-symplectic or log-symplectic manifolds). We end by studying symplectic structures with higher order singularities and updating theorems of Mazzeo, Melrose, and Radko from b-symplectic geometry to this more general context.

[发布机构] University of Michigan

[效力级别] Symplectic Geometry

[关键词] Toric Geometry;Symplectic Geometry;Mathematics;Science;Mathematics