English

Quantum cohomology of blowups

Algebraic Geometry 2025-02-05 v3 Symplectic Geometry

Abstract

We prove a decomposition theorem of the quantum cohomology D-module of the blowup of a smooth projective variety X along a smooth subvariety Z. The main tools we use are shift operators and Fourier analysis for equivariant quantum cohomology.

Keywords

Cite

@article{arxiv.2307.13555,
  title  = {Quantum cohomology of blowups},
  author = {Hiroshi Iritani},
  journal= {arXiv preprint arXiv:2307.13555},
  year   = {2025}
}

Comments

69 pages, 5 figures, v2: corrected minor errors and added Appendix B, v3: major revision; the main result has been strengthened by eliminating the variables x and y; the initial condition for the decomposition has been clarified; a discussion on the well-definedness of the pullbacks of quantum D-modules has been added