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

Gieseker, D.

J. Differ. Geom. 19, 173-206 (1984).

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

MSC:

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

Keywords:

moduli space; stable bundles of rank two and degree d; Chern class; De Rham cohomology