Frobenius Manifolds and Moduli Spaces for Singularities

by Claus Hertling

Overview

For those working in singularity theory or other areas of complex geometry, this volume will open the door to the study of Frobenius manifolds. In the first part Hertling explains the theory of manifolds with a multiplication on the tangent bundle. He then presents a simplified explanation of the role of Frobenius manifolds in singularity theory along with all the necessary tools and several applications. Readers will benefit from this careful and sound study of the fundamental structures and results in this exciting branch of mathematics.

Product Details

ISBN-13:	9780521812962
Publisher:	Cambridge University Press
Publication date:	07/25/2002
Series:	Cambridge Tracts in Mathematics , #151
Pages:	282
Product dimensions:	6.10(w) x 9.29(h) x 0.75(d)

Table of Contents

Part I. Multiplication on the Tangent Bundle: 1. Introduction to part 1; 2. Definition and first properties of F-manifolds; 3. Massive F-manifolds and Lagrange maps; 4. Discriminants and modality of F-manifolds; 5. Singularities and Coxeter groups; Part II. Frobenius Manifolds, Gauss-Manin Connections, and Moduli Spaces for Hypersurface Singularities: 6. Introduction to part 2; 7. Connections on the punctured plane; 8. Meromorphic connections; 9. Frobenius manifolds ad second structure connections; 10. Gauss-Manin connections for hypersurface singularities; 11. Frobenius manifolds for hypersurface singularities; 12. ∴μυ-constant stratum; 13. Moduli spaces for singularities; 14. Variance of the spectral numbers.

Editorial Reviews

'… a nice introduction to the theory of Frobenius manifolds …' Zentralblatt für Mathematik

'The book under review gives a very detailed analysis of the category of F-manifolds … the book is clean, rigorous and readable. the researchers in the areas of singularity theory, complex geometry, integrable systems, quantum cohomology, mirror symmetry and sympathetic geometry will find in this book a lot of useful information which has never been given in such detail before.' Proceedings of the Edinburgh Mathematical Society

'… one can say this book is a must for workers in the field of singularity theory.' Duco van Straten, Department of Mathematics, University of Mainz

From the Publisher

Addresses the relations between Frobenius manifolds and singularity theory, in two parts. The first section studies F-manifolds, discriminants, and Lagrange maps and their singularities, with some of Givental's work used as an application to prove a conjecture of Dubrovin about Frobenius manifolds and Coxeter groups. The second part takes up the construction of Frobenius manifolds in singularity theory, providing an elementary but detailed explanation, with results developed and cited. Suitable for readers with an understanding of the basic concepts of complex analytic geometry, including coherent sheaves and flatness. Annotation c. Book News, Inc., Portland, OR