Asian Journal of Mathematics

A mathematical theory of quantum sheaf cohomology

Ron Donagi, Josh Guffin, Sheldon Katz, and Eric Sharpe

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


The purpose of this paper is to present a mathematical theory of the half-twisted $(0, 2)$ gauged linear sigma model and its correlation functions that agrees with and extends results from physics. The theory is associated to a smooth projective toric variety $X$ and a deformation $\mathcal{E}$ of its tangent bundle $T_X$. It gives a quantum deformation of the cohomology ring of the exterior algebra of $\mathcal{E}*$. We prove that in the general case, the correlation functions are independent of "nonlinear" deformations. We derive quantum sheaf cohomology relations that correctly specialize to the ordinary quantum cohomology relations described by Batyrev in the special case $\mathcal{E} = T_X$.

Article information

Asian J. Math., Volume 18, Number 3 (2014), 387-418.

First available in Project Euclid: 8 September 2014

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 32L10: Sheaves and cohomology of sections of holomorphic vector bundles, general results [See also 14F05, 18F20, 55N30] 81T20: Quantum field theory on curved space backgrounds
Secondary: 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]

Quantum cohomology quantum shear cohomology toric varieties primitive collection gauged linear sigma model


Donagi, Ron; Guffin, Josh; Katz, Sheldon; Sharpe, Eric. A mathematical theory of quantum sheaf cohomology. Asian J. Math. 18 (2014), no. 3, 387--418.

Export citation