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.
Keywords
Cite
@article{arxiv.0810.4236,
title = {Orbifold quantum D-modules associated to weighted projective spaces},
author = {Martin A. Guest and Hironori Sakai},
journal= {arXiv preprint arXiv:0810.4236},
year = {2014}
}
Comments
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