The Newstead-Ramanan conjecture for Chern classes

2005/12/21 by Constantin Teleman, Teleman, Constantin, Christopher T. Woodward +1
Mathematics · #14H60 (Primary) #19L10 (Secondary) #19L47 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic Topology (math.AT) #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.math/0512486

openalex publication_date 2005/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Newstead and Ramanan conjectured the vanishing of the top (2g-1) Chern classes of the moduli space of stable, odd degree vector bundles of rank 2 on a Riemann surface of genus g. This was proved by Gieseker [G], while an analogue in rank 3 was recently settled by Kiem and Li [KL]. We generalise this to the vanishing of the top (g-1)r rational Chern classes of the moduli space M of stable principal bundles with semi-simple structure group of rank r, whenever M is a compact orbifold.

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