A degeneration of the moduli space of stable bundles. (English) Zbl 0557.14008

In the present paper the author has two aims: 1. He develops a method for investigating the topology of the smooth projective variety \(U_ Y\) of isomorphism classes of stable bundles of rank two and degree d (d is odd) on a smooth projective curve of genus \(g\geq 2\); 2. As an application of the above method he proves the following conjecture of Newstead and Ramanan: ”The k-th Chern class of the tangent bundle of \(U_ Y\) is zero in the De Rham cohomology of \(U_ Y\) if \(k>2g-2\) (the ground field is the field of complex numbers).”
Reviewer: V.Iliev


14F05 Sheaves, derived categories of sheaves, etc. (MSC2010)
14D20 Algebraic moduli problems, moduli of vector bundles
14F40 de Rham cohomology and algebraic geometry
14D15 Formal methods and deformations in algebraic geometry
Full Text: DOI