Combinatorial aspects of mirror symmetry

Simple item page
dc.creatorBatyrev, Victor
dc.creatorNill, Benjamin
dc.date2007-03-15
dc.date2007-04-26
dc.date.accessioned2026-07-07T10:05:52Z
dc.date.available2026-07-07T10:05:52Z
dc.descriptionThe purpose of this paper is to review some combinatorial ideas behind the mirror symmetry for Calabi-Yau hypersurfaces and complete intersections in Gorenstein toric Fano varieties. We suggest as a basic combinatorial object the notion of a Gorenstein polytope of index r. A natural combinatorial duality for d-dimensional Gorenstein polytopes of index r extends the well-known polar duality for reflexive polytopes (case r=1). We consider the Borisov duality between two nef-partitions as a duality between two Gorenstein polytopes P and P^* of index r together with selected special (r-1)-dimensional simplices S in P and S' in P^*. Different choices of these simplices suggest an interesting relation to Homological Mirror Symmetry.
dc.descriptionAMS-LaTeX, 37 pages, 3 figures; conjecture 4.10 refined, bibliography updated
dc.identifierhttps://arxiv.org/abs/math/0703456
dc.identifierhttp://arxiv.org/abs/math/0703456
dc.identifierContemporary Mathematics 452 (2008), 35-66
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/170140
dc.subjectCombinatorics
dc.subjectHigh Energy Physics - Theory
dc.subjectAlgebraic Geometry
dc.subject52B20, 14M25, 14J32
dc.titleCombinatorial aspects of mirror symmetry
dc.typetext

Files

Collections

arXiv