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1. CJM Online first
Orthogonal Bundles and Skew-Hamiltonian Matrices Using properties of skew-Hamiltonian matrices and classic
connectedness results, we prove that the moduli space
$M_{ort}^0(r,n)$ of stable rank $r$ orthogonal vector bundles
on $\mathbb{P}^2$, with Chern classes $(c_1,c_2)=(0,n)$, and trivial
splitting on the general line, is smooth irreducible of
dimension $(r-2)n-\binom{r}{2}$ for $r=n$ and $n \ge 4$, and
$r=n-1$ and $n\ge 8$. We speculate that the result holds in
greater generality.
Keywords:orthogonal vector bundles, moduli spaces, skew-Hamiltonian matrices Categories:14J60, 15B99 |
2. CJM 2014 (vol 66 pp. 961)
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 Categories:32L05, 14P25 |
3. 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 |
4. 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 Categories:14E05, 14J30 |
5. 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 Categories:58E15, 53C07 |