Vanishing of the top Chern classes of the moduli of vector bundles

2004/03/02 by Young‐Hoon Kiem, Young-Hoon Kiem, Jun Li +2
Mathematics · #14F25 #14F42 #14H60 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #math.AG #msc:14F25 #msc:14F42 #msc:14H60

paper · pdf · doi:10.48550/arxiv.math/0403033

openalex publication_date 2004/03/02 · arxiv created 2004/03/06 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let Y be a smooth projective curve of genus g≥ 2 and let M_r,d(Y) be the moduli space of stable vector bundles of rank r and degree d on Y. A classical conjecture of Newstead and Ramanan states that c_i(M_2,1(Y))=0 for i>2(g-1) i.e. the top 2g-1 Chern classes vanish. The purpose of this paper is to generalize this vanishing result to the rank 3 case by generalizing Gieseker's degeneration method. More precisely, we prove that c_i(M_3,1(Y))=0 for i>6g-5. In other words, the top 3g-3 Chern classes vanish. Notice that we also have c_i(M_3,2(Y))=0 for i>6g-5.

Related

• The Newstead-Ramanan conjecture for Chern classes
• Vanishing of top equivariant Chern classes of regular embeddings
• Universal Chern classes on the moduli of bundles
• The Index Formula on the Moduli of G-bundles
• Stability conditions on threefolds with vanishing Chern classes