Topic
Moduli space
About: Moduli space is a research topic. Over the lifetime, 15943 publications have been published within this topic receiving 410791 citations.
Papers published on a yearly basis
Papers
More filters
Book•
01 Jan 1965
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.
Abstract: “Geometric Invariant Theory” by Mumford/Fogarty (the first edition was published in 1965, a second, enlarged edition appeared in 1982) is the standard reference on applications of invariant theory to the construction of moduli spaces. This third, revised edition has been long awaited for by the mathematical community. It is now appearing in a completely updated and enlarged version with an additional chapter on the moment map by Prof. Frances Kirwan (Oxford) and a fully updated bibliography of work in this area. The book deals firstly with actions of algebraic groups on algebraic varieties, separating orbits by invariants and construction quotient spaces; and secondly with applications of this theory to the construction of moduli spaces. It is a systematic exposition of the geometric aspects of the classical theory of polynomial invariants.
2,695 citations
01 Jan 1985
TL;DR: This chapter discusses Brill-Noether theory on a moving curve, and some applications of that theory in elementary deformation theory and in tautological classes.
Abstract: Preface.- Guide to the Reader.- Chapter IX. The Hilbert Scheme.- Chapter X. Nodal curves.- Chapter XI. Elementary deformation theory and some applications.- Chapter XII. The moduli space of stable curves.- Chapter XIII. Line bundles on moduli.- Chapter XIV. The projectivity of the moduli space of stable curves.- Chapter XV. The Teichmuller point of view.- Chapter XVI. Smooth Galois covers of moduli spaces.- Chapter XVII. Cycles on the moduli spaces of stable curves.- Chapter XVIII. Cellular decomposition of moduli spaces.- Chapter XIX. First consequences of the cellular decomposition .- Chapter XX. Intersection theory of tautological classes.- Chapter XXI. Brill-Noether theory on a moving curve.- Bibliography.- Index.
2,597 citations
TL;DR: In this paper, the vacuum structure and dyon spectrum of N = 2 supersymmetric gauge theory in four dimensions, with gauge group SU(2), were studied. And the theory turns out to have remarkably rich and physical properties which can nonetheless be described precisely; exact formulas can be obtained, for instance, for electron and Dyon masses and the metric on the moduli space of vacua.
Abstract: We study the vacuum structure and dyon spectrum of N=2 supersymmetric gauge theory in four dimensions, with gauge group SU(2). The theory turns out to have remarkably rich and physical properties which can nonetheless be described precisely; exact formulas can be obtained, for instance, for electron and dyon masses and the metric on the moduli space of vacua. The description involves a version of Olive-Montonen electric-magnetic duality. The ``strongly coupled'' vacuum turns out to be a weakly coupled theory of monopoles, and with a suitable perturbation confinement is described by monopole condensation.
2,307 citations
Book•
01 Jan 1997TL;DR: In this paper, the Grauert-Mullich Theorem is used to define a moduli space for sheaves on K-3 surfaces, and the restriction of sheaves to curves is discussed.
Abstract: Preface to the second edition Preface to the first edition Introduction Part I. General Theory: 1. Preliminaries 2. Families of sheaves 3. The Grauert-Mullich Theorem 4. Moduli spaces Part II. Sheaves on Surfaces: 5. Construction methods 6. Moduli spaces on K3 surfaces 7. Restriction of sheaves to curves 8. Line bundles on the moduli space 9. Irreducibility and smoothness 10. Symplectic structures 11. Birational properties Glossary of notations References Index.
1,856 citations
TL;DR: In this article, it was shown that two natural approaches to quantum gravity coincide, relying on the equivalence of each approach to KdV equations, and they also investigated related mathematical problems.
Abstract: We show that two natural approaches to quantum gravity coincide. This identity is nontrivial and relies on the equivalence of each approach to KdV equations. We also investigate related mathematical problems.
1,756 citations