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

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1. CMB Online first

Takahashi, Tomokuni
 Projective plane bundles over an elliptic curve We calculate the dimension of cohomology groups for the holomorphic tangent bundles of each isomorphism class of the projective plane bundle over an elliptic curve. As an application, we construct the families of projective plane bundles, and prove that the families are effectively parametrized and complete. Keywords:projective plane bundle, vector bundle, elliptic curve, deformation, Kodaira-Spencer mapCategories:14J10, 14J30, 14D15

2. CMB Online first

Iena, Oleksandr; Leytem, Alain
 On the singular sheaves in the fine Simpson moduli spaces of $1$-dimensional sheaves In the Simpson moduli space $M$ of semi-stable sheaves with Hilbert polynomial $dm-1$ on a projective plane we study the closed subvariety $M'$ of sheaves that are not locally free on their support. We show that for $d\ge 4$ it is a singular subvariety of codimension $2$ in $M$. The blow up of $M$ along $M'$ is interpreted as a (partial) modification of $M\setminus M'$ by line bundles (on support). Keywords:Simpson moduli spaces, coherent sheaves, vector bundles on curves, singular sheavesCategory:14D20

3. CMB 2016 (vol 59 pp. 858)

Osserman, Brian
 Stability of Vector Bundles on Curves and Degenerations We introduce a weaker notion of (semi)stability for vector bundles on reducible curves which does not depend on a choice of polarization, and which suffices for many applications of degeneration techniques. We explore the basic properties of this alternate notion of (semi)stability. In a complementary direction, we record a proof of the existence of semistable extensions of vector bundles in suitable degenerations. Keywords:vector bundle, stability, degenerationCategories:14D06, 14H60

4. 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 groupCategories:14H60, 14D05, 14G15

5. 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 transformationCategories:58E20, 53C21

6. 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 genusCategories:14J60, 14C20, 14F05, 14J40
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