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 2011 (vol 63 pp. 616)
|A Modular Quintic Calabi-Yau Threefold of Level 55|
In this note we search the parameter space of Horrocks-Mumford quintic threefolds and locate a Calabi-Yau threefold that is modular, in the sense that the $L$-function of its middle-dimensional cohomology is associated with a classical modular form of weight 4 and level 55.
Keywords: Calabi-Yau threefold, non-rigid Calabi-Yau threefold, two-dimensional Galois representation, modular variety, Horrocks-Mumford vector bundle
Categories:14J15, 11F23, 14J32, 11G40
3. 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
4. CJM 2005 (vol 57 pp. 871)
|Hermitian Yang-_Mills--Higgs Metrics on\\Complete KÃ¤hler Manifolds |
In this paper, first, we will investigate the Dirichlet problem for one type of vortex equation, which generalizes the well-known Hermitian Einstein equation. Secondly, we will give existence results for solutions of these vortex equations over various complete noncompact K\"ahler manifolds.
Keywords:vortex equation, Hermitian Yang--Mills--Higgs metric,, holomorphic vector bundle, KÃ¤hler manifolds