Orbifold quantum D-modules associated to weighted projective spaces

Martin 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

    Fingerprint

    D-module
    Orbifold
    Weighted Spaces
    Projective Space
    Gromov-Witten Invariants
    Hypersurface
    Quantum Cohomology
    Grading
    Differential operator
    Factorization
    Intersection
    Decompose
    Cell

    Keywords

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

    ASJC Scopus subject areas

    • Mathematics(all)

    Cite this

    Orbifold quantum D-modules associated to weighted projective spaces. / Guest, Martin; Sakai, Hironori.

    In: Commentarii Mathematici Helvetici, Vol. 89, No. 2, 2014, p. 273-297.

    Research output: Contribution to journalArticle

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