1. CJM Online first
|Moduli Spaces of Vector Bundles over a Real Curve: $\mathbb Z/2$-Betti Numbers|
Moduli spaces of real bundles over a real curve arise naturally as Lagrangian submanifolds of the moduli space of semi-stable bundles over a complex curve. In this paper, we adapt the methods of Atiyah-Bott's ``Yang-Mills over a Riemann Surface'' to compute $\mathbb Z/2$-Betti numbers of these spaces.
Keywords:cohomology of moduli spaces, holomorphic vector bundles
2. CJM 2010 (vol 62 pp. 1201)
|Criteria for Very Ampleness of Rank Two Vector Bundles over Ruled Surfaces|
Very ampleness criteria for rank $2$ vector bundles over smooth, ruled surfaces over rational and elliptic curves are given. The criteria are then used to settle open existence questions for some special threefolds of low degree.
Keywords:vector bundles, very ampleness, ruled surfaces