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

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1. CMB 2013 (vol 57 pp. 439)

Yang, YanHong
The Fixed Point Locus of the Verschiebung on $\mathcal{M}_X(2, 0)$ for Genus-2 Curves $X$ in Charateristic $2$
We prove that for every ordinary genus-$2$ curve $X$ over a finite field $\kappa$ of characteristic $2$ with $\textrm{Aut}(X/\kappa)=\mathbb{Z}/2\mathbb{Z} \times S_3$, there exist $\textrm{SL}(2,\kappa[\![s]\!])$-representations of $\pi_1(X)$ such that the image of $\pi_1(\overline{X})$ is infinite. This result produces a family of examples similar to Laszlo's counterexample to de Jong's question regarding the finiteness of the geometric monodromy of representations of the fundamental group.

Keywords:vector bundle, Frobenius pullback, representation, etale fundamental group
Categories:14H60, 14D05, 14G15

2. CMB 2004 (vol 47 pp. 624)

Zhang, Xi
A Compactness Theorem for Yang-Mills Connections
In this paper, we consider Yang-Mills connections on a vector bundle $E$ over a compact Riemannian manifold $M$ of dimension $m> 4$, and we show that any set of Yang-Mills connections with the uniformly bounded $L^{\frac{m}{2}}$-norm of curvature is compact in $C^{\infty}$ topology.

Keywords:Yang-Mills connection, vector bundle, gauge transformation
Categories:58E20, 53C21

3. CMB 2001 (vol 44 pp. 452)

Ishihara, Hironobu
Some Adjunction Properties of Ample Vector Bundles
Let $\ce$ be an ample vector bundle of rank $r$ on a projective variety $X$ with only log-terminal singularities. We consider the nefness of adjoint divisors $K_X + (t-r) \det \ce$ when $t \ge \dim X$ and $t>r$. As an application, we classify pairs $(X,\ce)$ with $c_r$-sectional genus zero.

Keywords:ample vector bundle, adjunction, sectional genus
Categories:14J60, 14C20, 14F05, 14J40

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