Quantum cohomology via D-modules

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18 Citations (Scopus)

Abstract

We propose a new point of view on quantum cohomology, motivated by the work of Givental and Dubrovin, but closer to differential geometry than the existing approaches. The central object is a D-module which "quantizes" a commutative algebra associated to the (uncompactified) space of rational curves. Under appropriate conditions, we show that the associated flat connection may be gauged to the flat connection underlying quantum cohomology. This method clarifies the role of the Birkhoff factorization in the "mirror transformation", and it gives a new algorithm (requiring construction of a Groebner basis and solution of a system of o.d.e.) for computation of the quantum product.

Original languageEnglish
Pages (from-to)263-281
Number of pages19
JournalTopology
Volume44
Issue number2
DOIs
Publication statusPublished - 2005 Mar 1

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Keywords

  • Birkhoff factorization
  • D-module
  • Quantum cohomology

ASJC Scopus subject areas

  • Geometry and Topology

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