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Communications in Mathematical Physics

, Volume 164, Issue 3, pp 525–562 | Cite as

Gromov-Witten classes, quantum cohomology, and enumerative geometry

  • M. Kontsevich
  • Yu. Manin
Article

Abstract

The paper is devoted to the mathematical aspects of topological quantum field theory and its applications to enumerative problems of algebraic geometry. In particular, it contains an axiomatic treatment of Gromov-Witten classes, and a discussion of their properties for Fano varieties. Cohomological Field Theories are defined, and it is proved that tree level theories are determined by their correlation functions. Application to counting rational curves on del Pezzo surfaces and projective spaces are given.

Keywords

Field Theory Correlation Function Quantum Field Theory Tree Level Projective Space 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • M. Kontsevich
    • 1
  • Yu. Manin
    • 1
  1. 1.Max-Planck-Institut für MathematikBonnGermany

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