Cohomology of Moduli Spaces
Lead Research Organisation:
University of Oxford
Department Name: Mathematical Institute
Abstract
The study of complex algebraic curves, and how they vary in families, has been fundamental to algebraic geometry for at least the last century. Huge advances have been made in recent decades, and unexpected but extremely important links with theoretical physics and other parts of mathematics have been discovered. Nonetheless, in spite of 150 years of investigation, our understanding of the topology of the moduli spaces of curves is still very incomplete. The aim of this project is to gain new understanding of the topology of these and related moduli spaces, and also related moduli spaces of vector bundles over a varying curve, by representing them as quotients in the sense of geometric invariant theory and applying methods developed over the last twenty years for studying such quotients.
Organisations
People |
ORCID iD |
Frances Kirwan (Principal Investigator) |
Publications
Asok A
(2009)
A 1 -homotopy groups, excision, and solvable quotients
in Advances in Mathematics
Baldwin E
(2010)
A Geometric Invariant Theory Construction of Moduli Spaces of Stable Maps
in International Mathematics Research Papers
Baldwin E
(2008)
A GIT construction of moduli spaces of stable maps in positive characteristic
in Journal of the London Mathematical Society
Bérczi G
(2018)
Geometry of Moduli
Hoskins V
(2012)
Quotients of unstable subvarieties and moduli spaces of sheaves of fixed Harder-Narasimhan type
in Proceedings of the London Mathematical Society
Asok A
(2008)
Yang-Mills theory and Tamagawa numbers: the fascination of unexpected links in mathematics
in Bulletin of the London Mathematical Society