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Frobenius manifolds and moduli spaces for singularities / Claus Hertling

Auteur principal : Hertling, Claus, AuteurType de document : MonographieCollection : Cambridge tracts in mathematics, 151Langue : anglais.Pays : Grande Bretagne.Éditeur : Cambridge : Cambridge University Press, 2002Description : 1 vol. (270 p.) ; 24 cmISBN : 0521812968.ISSN : 0950-6284.Bibliographie : Bibliogr. p. 260-267. Index.Sujet MSC : 14J60, Algebraic geometry - Surfaces and higher-dimensional varieties, Vector bundles on surfaces and higher-dimensional varieties, and their moduli
14-02, Research exposition (monographs, survey articles) pertaining to algebraic geometry
14J17, Algebraic geometry - Surfaces and higher-dimensional varieties, Singularities of surfaces or higher-dimensional varieties
14B05, Local theory in algebraic geometry, Singularities
En-ligne : Zentralblatt | MathSciNet
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Frobenius manifolds are complex manifolds with an additional structure on the holomorphic tangent bundle: a multiplication and a metric which are compatible in a canonical way. They originate from physics and play a role in quantum cohomology and mirror symmetry. The book under review shows a beautiful application to singularity theory, the construction of global moduli spaces for isolated hypersurface singularities. The basis of the book is the author’s habilitation.

Part I of the book under review is devoted to the local structure of F-manifolds. They are closely related to singularity theory and symplectic geometry. ... Part II of the book is devoted to the construction of Frobenius manifolds in singularity theory. The base space of a semi-universal unfolding of an isolated hypersurface singularity can be equipped with the structure of a Frobenius manifold (results of K. Saito and M. Saito). ... (Zentralblatt)

Bibliogr. p. 260-267. Index

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