GromovWitten Theory of Toric Birational Transformations
Abstract
We investigate the effect of a general toric wall crossing on genus zero GromovWitten 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 AcostaShoemaker to the case of complete intersections in toric varieties, and generalizes some of the results of CoatesIritaniJiang on the crepant transformation conjecture to the setting of nonzero discrepancy.
 Publication:

arXiv eprints
 Pub Date:
 April 2016
 DOI:
 10.48550/arXiv.1604.03491
 arXiv:
 arXiv:1604.03491
 Bibcode:
 2016arXiv160403491A
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematical Physics;
 14N35;
 14A20;
 14E16;
 53D45
 EPrint:
 25 pages, typos corrected