Topology of moduli spaces of vector bundles on a real algebraic curve

Update: 2011-06-30

Description

Moduli spaces of real and quaternionic vector bundles on a curve can be expressed as Lagrangian quotients and embedded into the symplectic quotient corresponding to the moduli variety of holomorphic vector bundles of fixed rank and degree on a smooth complex projective curve. From the algebraic point of view, these Lagrangian quotients are irreducible sets of real points inside a complex moduli variety endowed with an anti-holomorphic involution. This presentation as a quotient enables us to generalise the equivariant methods of Atiyah and Bott to a setting with involutions, and compute the mod 2 Poincaré series of these real algebraic varieties. This is joint work with Chiu-Chu Melissa Liu (Columbia).

Comments

Top Podcasts

The Best New Comedy Podcast Right Now – June 2024 The Best News Podcast Right Now – June 2024 The Best New Business Podcast Right Now – June 2024 The Best New Sports Podcast Right Now – June 2024 The Best New True Crime Podcast Right Now – June 2024 The Best New Joe Rogan Experience Podcast Right Now – June 20 The Best New Dan Bongino Show Podcast Right Now – June 20 The Best New Mark Levin Podcast – June 2024

In Channel

Vector bundles and coherent systems on nodal curves

2011-07-2552:28

Higgs bundles and quaternionic geometry

2011-07-0401:05:32

Moduli spaces of locally homogeneous geometric structures

2011-07-0401:04:39

Bridgeland stability conditions and Fourier-Mukai transforms

2011-07-0101:03:12

Deligne-Hodge polynomials for SL(2,C)-character varieties of genus 1 and 2.

2011-07-0129:43

Derived equivalences of Azumaya algebras on K3 surfaces

2011-07-0130:29

Derived categories and rationality of conic bundles

2011-07-0126:56

Stability conditions for the local projective plane

2011-07-0152:06

Kahler-Einstein metrics and Geometric Invariant Theory

2011-07-0101:06:18

Introduction to moduli of varieties - IV: Surfaces of general type related to abelian varieties and hyperplane arrangements

2011-07-0101:05:24

Monopoles on the product of a surface and the circle

2011-06-3001:06:22

Vortices on Riemann Surfaces

2011-06-3001:05:08

Rank two Brill-Noether theory and the birational geometry of the moduli space of curves

2011-06-3001:06:31

Universal plane curve and moduli spaces of 1-dimensional coherent sheaves

2011-06-3026:23

Topology of moduli spaces of vector bundles on a real algebraic curve

2011-06-3031:19

Moduli of plane sheaves supported on curves of low multiplicity

2011-06-2929:10

Brill-Noether theory for vector bundles with fixed determinant

2011-06-2956:03

Geometric unitarity of the KZ/Hitchin connection on conformal blocks in genus 0

2011-06-2959:58

Refined curve counting on algebraic surfaces

2011-06-2901:02:01

Compactifications of reductive groups as moduli stacks of bundles

2011-06-2936:00

00:00

1.0x

Topology of moduli spaces of vector bundles on a real algebraic curve

#box-pro-ellipsis-173248276805617{-webkit-line-clamp:2;}Topology of moduli spaces of vector bundles on a real algebraic curve

Topology of moduli spaces of vector bundles on a real algebraic curve

Cambridge University

Topology of moduli spaces of vector bundles on a real algebraic curve