Type
Text
Type
Dissertation
Advisor
de Cataldo, Mark A | Varolin, Dror | Popa, Mihnea. | Schnell, Christian
Date
2016-12-01
Keywords
Mathematics
Department
Department of Mathematics
Language
en_US
Source
This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree.
Identifier
http://hdl.handle.net/11401/76385
Publisher
The Graduate School, Stony Brook University: Stony Brook, NY.
Format
application/pdf
Abstract
Let $S\to C$ be a smooth projective surface with numerically trivial canonical bundle fibered onto a curve. We prove the multiplicativity of the perverse filtration with respect to the cup product on $H^*(S^{[n]},\mathbb{Q})$ for the natural morphism $S^{[n]}\to C^{(n)}$. We also prove the multiplicativity for five families of Hitchin systems obtained in a similar way and compute the perverse numbers of the Hitchin moduli spaces. We show that for small values of $n$ the perverse numbers match the predictions of the numerical version of the de Cataldo-Hausel-Migliorini $P=W$ conjecture and of the conjecture by Hausel-Letellier-Villegas. | 48 pages
Recommended Citation
Zhang, Zili, "Multiplicativity of perverse filtration for Hilbert schemes of fibered surfaces" (2016). Stony Brook Theses and Dissertations Collection, 2006-2020 (closed to submissions). 2309.
https://commons.library.stonybrook.edu/stony-brook-theses-and-dissertations-collection/2309