The Mumford relations and the moduli of rank three stable bundles

DOI10.1023/A:1000101030261zbMATH Open0915.14008arXivalg-geom/9503023MaRDI QIDQ4360120

Richard Earl

Publication date: 28 June 1999

Published in: Compositio Mathematica (Search for Journal in Brave)

Abstract: We find a complete set of relations for the rational cohomology ring of the moduli space of rank three stable bundles over a Riemann surface of genus g and also show that the Pontryagin ring vanishes in degree 12g-8 and greater. The results are obtained by introducing some 'dual' Mumford relations and generalising Kirwan's proofs of the Mumford and Newstead conjectures in the rank two case. (In this revised version of the paper the vanishing degree of the Pontryagin ring of the moduli space has been improved from `in and above degree 12g-4' to `in and above degree 12g-8'. This degree is now known to be sharp.)

Full work available at URL: https://arxiv.org/abs/alg-geom/9503023

zbMATH Keywords

moduli spacecompact Riemann surfaceMumford relationsdual relationsrelations for the cohomology ring

Mathematics Subject Classification ID

Algebraic moduli problems, moduli of vector bundles (14D20) Classical real and complex (co)homology in algebraic geometry (14F25)

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