Vanishing of top equivariant Chern classes of regular embeddings

2005/03/10 by Michel Brion, Brion, Michel, Ivan Kausz +1
Mathematics · #14H60 #14L30 #14M17 #55N91 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.math/0503196

openalex publication_date 2005/03/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a connected affine algebraic group and X a regular G-variety (in the sense of Bifet-De Concini-Procesi) with open orbit G/H and boundary divisor D. We show the vanishing of the G-equivariant Chern classes of the bundle of differential forms on X with logarithmic poles along D, in degrees larger than dim(X) - \rk(G) + \rk(H). Our motivation comes from Gieseker's degeneration method to prove the Newstead-Ramanan conjecture on the vanishing of the top Chern classes of the moduli space of stable vector bundles on a curve.

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