Journal ArticleDOI
The Yang-Mills equations over Riemann surfaces
Michael Atiyah,Raoul Bott +1 more
Reads0
Chats0
TLDR
In this article, the Yang-Mills functional over a Riemann surface is studied from the point of view of Morse theory, and the main result is that this is a perfect 9 functional provided due account is taken of its gauge symmetry.Abstract:
The Yang-Mills functional over a Riemann surface is studied from the point of view of Morse theory. The main result is that this is a ‘perfect9 functional provided due account is taken of its gauge symmetry. This enables topological conclusions to be drawn about the critical sets and leads eventually to information about the moduli space of algebraic bundles over the Riemann surface. This in turn depends on the interplay between the holomorphic and unitary structures, which is analysed in detail.read more
Citations
More filters
Journal ArticleDOI
Birational Equivalences of Vortex Moduli
Steven B. Bradlow,Steven B. Bradlow,Steven B. Bradlow,Georgios Daskalopoulos,Georgios Daskalopoulos,Georgios Daskalopoulos,Richard Wentworth,Richard Wentworth,Richard Wentworth +8 more
TL;DR: In this article, a finite-dimensional Kahler manifold with a holomorphic, symplectic circle action whose reduced spaces may be identified with the τ-vortex moduli spaces (or τ-stable pairs) was constructed.
Journal ArticleDOI
Semistable principal bundles—I (characteristic zero)
V. Balaji,C.S. Seshadri +1 more
TL;DR: In this paper, Tannakian showed that the moduli functor associated to semistable principal G-bundles is proper, i.e., it can be viewed as an atensor functor.
Journal ArticleDOI
Modified pure spinors and mirror symmetry
Pascal Grange,Ruben Minasian +1 more
TL;DR: In this paper, it has been shown that quantities involved in stability conditions for topological D-branes, and containing gauge fields in their expressions, are exchanged by mirror symmetry, which can be considered as an open-string version of the mirror symmetry between pure spinors.
Posted Content
The moment-weight inequality and the Hilbert-Mumford criterion
TL;DR: In this paper, the authors give an essentially self-contained exposition of geometric invariant theory from a differential geometric viewpoint, including the moment-weight inequality, the negative gradient flow of the moment map squared and the Kempf-Ness function.
Journal ArticleDOI
A symplectic geometry approach to generalized Casson's invariants of 3-manifolds
TL;DR: In this article, an integer valued invariant XG(M ) was proposed for an arbitrary oriented rational homology 3-sphere (RHS), which is defined for homology lens spaces.
References
More filters
Book
Principles of Algebraic Geometry
Phillip Griffiths,Joe Harris +1 more
TL;DR: In this paper, a comprehensive, self-contained treatment of complex manifold theory is presented, focusing on results applicable to projective varieties, and including discussion of the theory of Riemann surfaces and algebraic curves, algebraic surfaces and the quadric line complex.
Book
Inequalities: Theory of Majorization and Its Applications
TL;DR: In this paper, Doubly Stochastic Matrices and Schur-Convex Functions are used to represent matrix functions in the context of matrix factorizations, compounds, direct products and M-matrices.
Book
Geometric Invariant Theory
TL;DR: Geometric invariant theory for moduli spaces has been studied extensively in the mathematical community as mentioned in this paper, with a large number of applications to the moduli space construction problem, see, for instance, the work of Mumford and Fogarty.
Journal ArticleDOI
Self-duality in four-dimensional Riemannian geometry
TL;DR: In this article, the authors present a self-contained account of the ideas of R. Penrose connecting four-dimensional Riemannian geometry with three-dimensional complex analysis, and apply this to the self-dual Yang-Mills equations in Euclidean 4-space and compute the number of moduli for any compact gauge group.
Journal ArticleDOI
Stable and unitary vector bundles on a compact Riemann surface
M. S. Narasimhan,C. S. Seshadri +1 more
TL;DR: In this article, it was shown that on the space of isomorphic classes of unitary vector bundles on X of a given rank, there is a natural structure of a normal projective variety (Theorem 8.1).