Torus Actions and Singularities in Symplectic Geometry.

Toric Geometry;Symplectic Geometry;Mathematics;Science;Mathematics

Scott, Geoffrey StephenGuillemin, Victor ;

University of Michigan

关键词: Toric Geometry;    Symplectic Geometry;    Mathematics;    Science;    Mathematics;   

Others  :  https://deepblue.lib.umich.edu/bitstream/handle/2027.42/107059/gsscott_1.pdf?sequence=1&isAllowed=y

瑞士|英语

来源: The Illinois Digital Environment for Access to Learning and Scholarship

【 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.