Filtrations on equivariant quantum cohomology and Hilbert-Poincar\'e series
Symplectic Geometry
2024-11-13 v2 Algebraic Geometry
Abstract
We prove that Floer theory induces a filtration by ideals on equivariant quantum cohomology of symplectic manifolds equipped with a -action. In particular, this gives rise to Hilbert-Poincar\'e polynomials on ordinary cohomology that depend on Floer theory. En route, the paper develops structural properties of filtrations on three versions of equivariant Floer cohomology. We obtain an explicit presentation for equivariant symplectic cohomology in the Calabi-Yau and Fano settings.
Keywords
Cite
@article{arxiv.2410.17237,
title = {Filtrations on equivariant quantum cohomology and Hilbert-Poincar\'e series},
author = {Alexander F. Ritter and Filip Živanović},
journal= {arXiv preprint arXiv:2410.17237},
year = {2024}
}
Comments
72 pages, 12 figures, fixed Theorem 1.10 and 14.3, new Remark 1.12 about the persistence module, very minor other changes