4,863 research outputs found
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
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
Master Spaces for stable pairs
We construct master spaces for oriented torsion free sheaves coupled with
morphisms into a fixed reference sheaf. These spaces are projective varieties
endowed with a natural \C^*-action. The fixed point set of this action
contains the moduli space of semistable oriented torsion free sheaves and the
quot scheme associated with the given data.
In the case of curves with trivial reference sheaf, our master spaces
compactify the moduli spaces constructed by Bertram, Daskalopoulos and
Wentworth. In the 2-dimensional case with trivial rank 1 reference sheaf,
master spaces provide algebraic analoga of compactified moduli spaces of
twisted quaternionic monopoles.Comment: 26 pages. New introduction and applications LaTeX2
Foundational Extensible Corecursion
This paper presents a formalized framework for defining corecursive functions
safely in a total setting, based on corecursion up-to and relational
parametricity. The end product is a general corecursor that allows corecursive
(and even recursive) calls under well-behaved operations, including
constructors. Corecursive functions that are well behaved can be registered as
such, thereby increasing the corecursor's expressiveness. The metatheory is
formalized in the Isabelle proof assistant and forms the core of a prototype
tool. The corecursor is derived from first principles, without requiring new
axioms or extensions of the logic
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