dc.contributor.author Smith, Ivan en dc.contributor.author Sheridan, Nick en dc.date.accessioned 2020-11-03T00:31:21Z dc.date.available 2020-11-03T00:31:21Z dc.identifier.issn 0020-9910 dc.identifier.uri https://www.repository.cam.ac.uk/handle/1810/312354 dc.description.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. dc.publisher Springer Nature dc.rights All rights reserved dc.rights.uri dc.title Homological mirror symmetry for generalized Greene-Plesser mirrors en dc.type Article prism.publicationName Inventiones Mathematicae en dc.identifier.doi 10.17863/CAM.59446 dcterms.dateAccepted 2020-10-30 en rioxxterms.version AM rioxxterms.licenseref.uri http://www.rioxx.net/licenses/all-rights-reserved en rioxxterms.licenseref.startdate 2020-10-30 en rioxxterms.type Journal Article/Review en pubs.funder-project-id EPSRC (EP/N01815X/1) cam.issuedOnline 2020-11-14 en cam.orpheus.success Mon Nov 30 07:31:00 GMT 2020 - Embargo updated * cam.orpheus.counter 7 * rioxxterms.freetoread.startdate 2021-11-14
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