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July 2014 A mathematical theory of quantum sheaf cohomology
Ron Donagi, Josh Guffin, Sheldon Katz, Eric Sharpe
Asian J. Math. 18(3): 387-418 (July 2014).


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 $\mathcal{E} = T_X$.


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Ron Donagi. Josh Guffin. Sheldon Katz. Eric Sharpe. "A mathematical theory of quantum sheaf cohomology." Asian J. Math. 18 (3) 387 - 418, July 2014.


Published: July 2014
First available in Project Euclid: 8 September 2014

zbMATH: 1300.32022
MathSciNet: MR3257832

Primary: 32L10 , 81T20
Secondary: 14N35

Keywords: gauged linear sigma model , primitive collection , quantum cohomology , quantum shear cohomology , toric varieties

Rights: Copyright © 2014 International Press of Boston


Vol.18 • No. 3 • July 2014
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