Orbifold quantum D-modules associated to weighted projective spaces

Abstract

We construct in an abstract fashion the orbifold quantum cohomology (quantum orbifold cohomology) of weighted projective space, starting from the orbifold quantum 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 to the more difficult case of Fano hypersurfaces in weighted projective space. However, in contrast to the case of weighted projective space itself or a Fano hypersurface in projective space, a "small Birkhoff cell" can appear in the construction; we give an example of this phenomenon.

24 pages. The main modification in this (final) version is the description of an ambiguity in the example of section 5, which was omitted from the original version

References in corpus (1)

• Quantum D-modules and equivariant Floer theory for free loop spaces

Cited by in corpus (8)

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• The Full Orbifold $K$-theory of Abelian Symplectic Quotients
• The small quantum cohomology of a weighted projective space, a mirror D-module and their classical limits
• Torsion in the full orbifold K-theory of abelian symplectic quotients
• Some tt* structures and their integral Stokes data