Holomorphic symplectic manifolds from finite group actions on moduli spaces of sheaves
File(s)
Author(s)
Carini, Riccardo
Type
Thesis
Abstract
We explore the prospect of finding examples of holomorphic symplectic mani- folds by exploiting finite symplectic group actions on moduli spaces of semistable sheaves on symplectic surfaces. Specifically, in the context of the local symplectic surface given by the cotangent bundle of a smooth hyperelliptic curve of genus 3, we get an affirmative outcome. Namely, we show that the quotient of the moduli space of rank two Higgs bundles with fixed determinant by the hyperelliptic in- volution admits a crepant resolution given by the blow-up of its reduced singular locus. Furthermore, we discuss potential extensions of our results to compact symplectic surfaces.
Version
Open Access
Date Issued
2023-07-25
Date Awarded
01/11/2023
License URL
Advisor
Thomas, Richard
Sponsor
Engineering and Physical Sciences Research Council
Grant Number
EP/S021590/1
Publisher Department
Mathematics
Publisher Institution
Imperial College London
Qualification Level
Doctoral
Qualification Name
Doctor of Philosophy (PhD)