Fano mirror periods from the Frobenius structure conjecture
Abstract
The Fano classification program proposed by CoatesCortiGalkinGolyshevKasprzyk is based on the mirror symmetry prediction that the regularized quantum period of a Fano should be equivalent to the classical period of its mirror LandauGinzburg potential. We prove that this mirror equivalence follows from versions of the Frobenius structure conjecture of GrossHackingKeel. We also find that the regularized quantum period, which is defined in terms of descendant GromovWitten numbers, is in fact given by certain naive curve counts.
 Publication:

arXiv eprints
 Pub Date:
 March 2019
 arXiv:
 arXiv:1903.12014
 Bibcode:
 2019arXiv190312014M
 Keywords:

 Mathematics  Algebraic Geometry;
 14J33 (Primary) 14J45;
 14N35 (Secondary)
 EPrint:
 11 pages