Conformal field theory and the cohomology of the moduli space of stable bundles
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 \(N_ g\).
scientific article; zbMATH DE number 120198