Normal generation of vector bundles over a curve

On the Rational Homotopy Type of a Moduli Space of Vector Bundles over a Curve

We study the rational homotopy of the moduli space NX of stable vector bundles of rank two and fixed determinant of odd degree over a compact connected Riemann surface X of genus g ≥ 2. The symplectic group Aut(H1(X,Z)) ∼= Sp(2g,Z) has a natural action on the rational homotopy groups πn(NX)⊗ZQ. We prove that this action extends to an action of Sp(2g,C) on πn(NX)⊗ZC. We also show that πn(NX)⊗ZC ...

Rationality of the Moduli Space of Vector Bundles over a Smooth Curve

This article contains a survey on the conjectured rationality of the moduli space of vector bundles over a smooth curve. The main result is a new proof of stable rationality, which implies Conjecture 1 (stated below) for a large number of cases. We describe the progress which had been made on this problem by Tyurin and Newstead, and explain why the proof does not work in general. Ballico rejuve...

Rank four vector bundles without theta divisor over a curve of genus two

We show that the locus of stable rank four vector bundles without theta divisor over a smooth projective curve of genus two is in canonical bijection with the set of theta-characteristics. We give several descriptions of these bundles and compute the degree of the rational theta map.

The Moduli Space of Stable Vector Bundles over a Real Algebraic Curve

We study the spaces of stable real and quaternionic vector bundles on a real algebraic curve. The basic relationship is established with unitary representations of an extension of Z/2 by the fundamental group. By comparison with the space of real or quaternionic connections, some of the basic topological invariants of these spaces are calculated.

Vector bundles over algebraic curves