Gromov-Witten Theory of Toric Birational Transformations

Abstract

We investigate the effect of a general toric wall crossing on genus zero Gromov-Witten theory. Given two complete toric orbifolds $X_{+}$ and $X_{-}$ related by wall crossing under variation of GIT, we prove that their respective $I$-functions are related by linear transformation and asymptotic expansion. We use this comparison to deduce a similar result for birational complete intersections in $X_{+}$ and $X_{-}$. This extends the work of the previous authors in Acosta-Shoemaker to the case of complete intersections in toric varieties, and generalizes some of the results of Coates-Iritani-Jiang on the crepant transformation conjecture to the setting of non-zero discrepancy.

25 pages, typos corrected