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Search: All articles in the CJM digital archive with keyword vector bundle

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1. CJM 2015 (vol 67 pp. 961)

Abuaf, Roland; Boralevi, Ada
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)

Baird, Thomas
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)

Lee, Edward
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)

Alzati, Alberto; Besana, Gian Mario
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)

Zhang, Xi
Hermitian Yang-_Mills--Higgs Metrics on\\Complete Kähler 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, Kähler manifolds
Categories:58E15, 53C07

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