467 research outputs found
The Coupled Seiberg-Witten Equations, vortices, and Moduli spaces of stable pairs
We introduce coupled Seiberg-Witten equations, and we prove, using a
generalized vortex equation, that, for Kaehler surfaces, the moduli space of
solutions of these equations can be identified with a moduli space of
holomorphic stable pairs. In the rank 1 case, one recovers Witten's result
identifying the space of irreducible monopoles with a moduli space of divisors.
As application, we give a short proof of the fact that a rational surface
cannot be diffeomorphic to a minimal surface of general type.Comment: late
A wall crossing formula for degrees of real central projections
The main result is a wall crossing formula for central projections defined on
submanifolds of a real projective space. Our formula gives the jump of the
degree of such a projection when the center of the projection varies. The fact
that the degree depends on the projection is a new phenomenon, specific to real
algebraic geometry. We illustrate this phenomenon in many interesting
situations. The crucial assumption on the class of maps we consider is relative
orientability, a condition which allows us to define a -valued degree map
in a coherent way. We end the article with several examples, e.g. the pole
placement map associated with a quotient, the Wronski map, and a new version of
the real subspace problem.Comment: 29 pages. First revised version: The proof of the "wall-crossing
formula" is now more conceptional. We prove new general properties of the set
of values of the degree map on the set of central projections. Second revised
version: minor corrections. To appear in International Journal of Mathematic
Seiberg-Witten invariants for manifolds with , and the universal wall crossing formula
In this paper we describe the Seiberg-Witten invariants, which have been
introduced by Witten, for manifolds with . In this case the invariants
depend on a chamber structure, and there exists a universal wall crossing
formula. For every K\"ahler surface with and =0, these invariants
are non-trivial for all -structures of non-negative index.Comment: LaTeX, 27 pages. To appear in Int. J. Mat
Real determinant line bundles
This article is an expanded version of the talk given by Ch. O. at the Second
Latin Congress on "Symmetries in Geometry and Physics" in Curitiba, Brazil in
December 2010. In this version we explain the topological and gauge-theoretical
aspects of our paper "Abelian Yang-Mills theory on Real tori and Theta divisors
of Klein surfaces".Comment: LaTeX, 8 page
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