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The Pontryagin rings of moduli spaces of arbitrary rank holomorphic bundles over a Riemann surface

Richard Earl·Frances Kirwan
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Abstract

The cohomology of the moduli spaces of stable bundles M(n,d), of coprime rank n and degree d, over a Riemann surface (of genus g > 1) have been intensely studied over the past three decades. We prove in this paper that the Pontryagin ring of M(n,d) vanishes in degrees above 2n(n-1)(g-1) and that this bound is strict (i.e. there exists a non-zero element of degree 2n(n-1)(g-1) in Pont(M(n,d)).) This result is a generalisation of a 1967 Newstead conjecture that Pont(M(2,1)) vanished above 4(g-1) (or equivalently that β^g =0.) These results have been independently proved by Lisa Jeffrey and Jonathan Weitsman.

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Richard Earl, Frances Kirwan. 1997-09-10. The Pontryagin rings of moduli spaces of arbitrary rank holomorphic bundles over a Riemann surface. https://arxiv.org/abs/alg-geom/9709012

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