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


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.


Field Theory Correlation Function Quantum Field Theory Tree Level Projective Space 
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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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