English

Narrow quantum D-modules and quantum Serre duality

Algebraic Geometry 2020-10-27 v3

Abstract

Given Y a non-compact manifold or orbifold, we define a natural subspace of the cohomology of Y called the narrow cohomology. We show that despite Y being non-compact, there is a well-defined and non-degenerate pairing on this subspace. The narrow cohomology proves useful for the study of genus zero Gromov-Witten theory. When Y is a smooth complex variety or Deligne-Mumford stack, one can define a quantum D-module on the narrow cohomology of Y. This yields a new formulation of quantum Serre duality.

Keywords

Cite

@article{arxiv.1811.01888,
  title  = {Narrow quantum D-modules and quantum Serre duality},
  author = {Mark Shoemaker},
  journal= {arXiv preprint arXiv:1811.01888},
  year   = {2020}
}

Comments

Final version. To appear in Ann. Inst. Fourier

R2 v1 2026-06-23T05:04:49.422Z