Conformal field theory and the cohomology of the moduli space of stable bundles
type: Item
instance of: scholarly article
title: Conformal field theory and the cohomology of the moduli space of stable bundles
zbMATH Open document ID: 0772.53013
author: Michael Thaddeus
published in: Journal of Differential Geometry
publication date: 1993-02-18T00:00:00Z
review text: Let \(\Sigma_ g\) be a compact Riemann surface of genus \(g \geq 2\) and let \(E\) be a line bundle over \(\Sigma_ g\) of degree one. Let \(N_ g\) denote the smooth variety given by the moduli space for stable bundles, \(V\), over \(\Sigma_ g\) such that \(\Lambda^ 2V \equiv E\). The author uses a ``twisting'' of the \(SU(2)\) Wess-Zumino-Witten model from mathematical physics to compute \(H^*(N_ g;\mathbb{Q})\). The WZW-method (twisted to apply to degree-one bundles) calculates \(\dim H^ 0(N_ g;L^ k)\) and enables the author to study products of the generators of \(H^*(N_ g;\mathbb{Q})\) given in [\textit{P. E. Newstead}, Topology 6, 241-262 (1967; Zbl 0201.234)]. As corollaries, the author proves Newstead's conjecture that \(p^ g_ 1(N_ g) = 0\) and obtains a formula for the volume of \(N_ g\).
Mathematics Subject Classification ID: 53C07
Mathematics Subject Classification ID: 55R40
zbMATH DE Number: 120198
zbMATH Keywords: Wess-Zumino-Witten model
zbMATH Keywords: Newstead's conjecture
reviewed by: Victor P. Snaith
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.4310/jdg/1214447808
OpenAlex ID: W1580088620
Wikidata QID: Q115181390
DOI: 10.4310/JDG/1214447808
description: scientific article; zbMATH DE number 120198