arXiv subjects

Oscar Garcia-Prada

Publications and source records attributed to Oscar Garcia-Prada.

40 records · Page 3Linked to original sources

arXiv1996

Non-abelian monopoles and vortices

The Seiberg-Witten equations are defined on certain complex line bundles over smooth oriented four manifolds. When the base manifold is a complex Kahler surface, the Seiberg-Witten equations are essentially the Abelian vortex equations. Using known non-abelian generalizations of the vortex equations as a guide, we explore some non-abelian versions of the Seiberg-Witten equations. We also make some comments about the differences between the vortex equations that have previously appeared in the literature and those that emerge as Kahler versions of Seiberg-witten type equations.

alg-geom↗

arXiv1996

A Hitchin-Kobayashi Correspondence for Coherent Systems on Riemann Surfaces

A `coherent system' $(\Cal E,V)$, consists of a holomorphic bundle plus a linear subspace of its space of holomorphic sections. Based on the usual notion in Geometric Invariant Theory, a notion of slope stability has been defined for such objects (by Le Potier, and also by Rhagavendra and Vishwanath). In this paper we show that stability in this sense is equivalent to the existence of solutions to a certain set of gauge theoretic equations. One of the equations is essentially the vortex equation (i.e. the Hermitian-Einstein equation with an additional zeroth order term), and the other is an orthonormality condition on a frame for the subspace $V\subset H^0(\Cal E)$.

alg-geom↗

arXiv1995

Higher cohomology triples and holomorphic extensions

We introduce equations for special metrics, and notions of stability for some new types of augmented holomorphic bundles. These new examples include holomorphic extensions, and in this case we prove a Hitchin-Kobayashi correspondence between a certain deformation of the Hermitian-Einstein equations and our definition of stability for an extension.

alg-geom↗

arXiv1994

Stable triples, equivariant bundles and dimensional reduction

This is a resubmission of preprint 9401008 , which has some TeXnical errors introduced by the "reform" procedure (designed to avoid precisely these problems!). The original can be formatted by editing out the messages "%% following line cannot be broken..." at line 1674. This problem has been corrected in the current version. The content of the paper has not been changed in any way. My aplogies for any inconvenience caused. SB

alg-geom↗