Homological mirror symmetry for generalized Greene-Plesser mirrors
Abstract
We prove Kontsevich's homological mirror symmetry conjecture for certain mirror pairs arising from Batyrev-Borisov's `dual reflexive Gorenstein cones' construction. In particular we prove HMS for all Greene-Plesser mirror pairs (i.e., Calabi-Yau hypersurfaces in quotients of weighted projective spaces). We also prove it for certain mirror Calabi-Yau complete intersections arising from Borisov's construction via dual nef partitions, and also for certain Calabi-Yau complete intersections which do not have a Calabi-Yau mirror, but instead are mirror to a Calabi-Yau subcategory of the derived category of a higher-dimensional Fano variety. The latter case encompasses Kuznetsov's `K3 category of a cubic fourfold', which is mirror to an honest K3 surface; and also the analogous category for a quotient of a cubic sevenfold by an order-3 symmetry, which is mirror to a rigid Calabi-Yau threefold.
Keywords
Cite
@article{arxiv.1709.08937,
title = {Homological mirror symmetry for generalized Greene-Plesser mirrors},
author = {Nick Sheridan and Ivan Smith},
journal= {arXiv preprint arXiv:1709.08937},
year = {2020}
}
Comments
43 pages, 1 figure; introduction reorganized and additional examples included, other minor changes. Final version, to appear in Invent. Math