The Picard group of the moduli space of sheaves on a quadric surface
Open Access
Author:
Pedchenko, Dmitrii
Graduate Program:
Mathematics
Degree:
Doctor of Philosophy
Document Type:
Dissertation
Date of Defense:
February 25, 2021
Committee Members:
Jack William Huizenga, Dissertation Advisor/Co-Advisor Jack William Huizenga, Committee Chair/Co-Chair Yuriy G Zarkhin, Committee Member John Lesieutre, Committee Member Martin Bojowald, Outside Member Alexei Novikov, Program Head/Chair
Keywords:
Mathematics Algebraic Geometry Moduli spaces of sheaves Picard group Vector Bundles
Abstract:
In this dissertation, we study the Picard group of the moduli space of semistable sheaves on a smooth quadric surface. We polarize the surface by an ample divisor close to the anticanonical class. We focus especially on moduli spaces of sheaves of small discriminant, where we observe new and interesting behavior. Our method relies on constructing certain resolutions for semistable sheaves and applying techniques of geometric invariant theory to the resulting families of sheaves.