Orbifold quantum D-modules associated to weighted projective spaces

Martin A. Guest, Hironori Sakai

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

We construct in an abstract fashion (without using Gromov-Witten invariants) the orbifold quantum cohomology of weighted projective space, starting from a certain differential operator. We obtain the product, grading, and intersection form by making use of the associated self-adjoint D-module and the Birkhoff factorization procedure. The method extends inprinciple to the more difficult case of Fano hypersurfaces in weighted projective space, where Gromov-Witten invariants have not yet been computed, and we illustrate this by means of an example originally studied by A. Corti. In contrast to the case of weighted projective space itself or the case of a Fano hypersurface in projective space, a "small cell" of the Birkhoff decomposition plays a role in the calculation.

Original languageEnglish
Pages (from-to)273-297
Number of pages25
JournalCommentarii Mathematici Helvetici
Volume89
Issue number2
DOIs
Publication statusPublished - 2014

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Keywords

  • Birkhoff decomposition
  • D-module
  • Quantum cohomology
  • Weighted projective space

ASJC Scopus subject areas

  • Mathematics(all)

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