Homological mirror symmetry for generalized Greene-Plesser mirrors
Accepted version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
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