On the Quantum Cohomology of Fano Toric Manifolds and the Intersection Cohomology of Singular Symplectic Quotients

The second result computes the intersection cohomology of the singular symplectic reduced spaces. Let M be a closed symplectic manifold with a Hamiltonian S1-action defined on it and mu is the moment map. If 0 is a singular value of mu, the reduced space mu-1(0)/S1 is, in general, no longer an orbifold but contains singularities. We show that there is a surjective map from the equivariant cohomology of M to the intersection cohomology of mu-1(0)/ S1. This result can be considered as a symplectic generalization of the Beilinson-Bernstein-Deligne-Gabor decomposition theorem for singular algebraic varieties. Using this surjectivity result and the localization technique, we can relate the pairings of the intersection cohomology classes to the equivariant cohomology classes in M. We show that a theorem of Kalkman has a direct generalization in the singular setting.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Ho, Jeffrey

Contributors dc:contributor

• Richard Bishop

• Mathematics

Language dc:language

eng

Identifier

(MiAaPQ)AAI9953047

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/86983