| dc.identifier.uri | http://hdl.handle.net/11401/76385 | |
| dc.description.sponsorship | This work is sponsored by the Stony Brook University Graduate School in compliance with the requirements for completion of degree. | en_US |
| dc.format | Monograph | |
| dc.format.medium | Electronic Resource | en_US |
| dc.language.iso | en_US | |
| dc.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dc.type | Dissertation | |
| dcterms.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. | |
| dcterms.available | 2017-09-20T16:50:09Z | |
| dcterms.contributor | de Cataldo, Mark A | en_US |
| dcterms.contributor | Varolin, Dror | en_US |
| dcterms.contributor | Schnell, Christian | en_US |
| dcterms.contributor | Popa, Mihnea. | en_US |
| dcterms.creator | Zhang, Zili | |
| dcterms.dateAccepted | 2017-09-20T16:50:09Z | |
| dcterms.dateSubmitted | 2017-09-20T16:50:09Z | |
| dcterms.description | Department of Mathematics | en_US |
| dcterms.extent | 48 pg. | en_US |
| dcterms.format | Application/PDF | en_US |
| dcterms.format | Monograph | |
| dcterms.identifier | http://hdl.handle.net/11401/76385 | |
| dcterms.issued | 2016-12-01 | |
| dcterms.language | en_US | |
| dcterms.provenance | Made available in DSpace on 2017-09-20T16:50:09Z (GMT). No. of bitstreams: 1
Zhang_grad.sunysb_0771E_12835.pdf: 513183 bytes, checksum: d716fa773382a30476352d861b2f3a1c (MD5)
Previous issue date: 1 | en |
| dcterms.publisher | The Graduate School, Stony Brook University: Stony Brook, NY. | |
| dcterms.subject | Mathematics | |
| dcterms.title | Multiplicativity of perverse filtration for Hilbert schemes of fibered surfaces | |
| dcterms.type | Dissertation | |
