On smooth Gorenstein polytopes
2015 (English)In: Tohoku mathematical journal, ISSN 0040-8735, Vol. 67, no 4, 513-530 p.Article in journal (Refereed) Published
A Gorenstein polytope of index r is a lattice polytope whose rth dilate is a reflexive polytope. These objects are of interest in combinatorial commutative algebra and enumerative combinatorics, and play a crucial role in Batyrev's and Borisov's computation of Hodge numbers of mirror-symmetric generic Calabi-Yau complete intersections. In this paper we report on what is known about smooth Gorenstein polytopes, i.e., Gorenstein polytopes whose normal fan is unimodular. We classify d-dimensional smooth Gorenstein polytopes with index larger than (d + 3)/3. Moreover, we use a modification of Obro's algorithm to achieve classification results for smooth Gorenstein polytopes in low dimensions. The first application of these results is a database of all toric Fano d-folds whose anticanonical divisor is divisible by an integer r satisfying r >= d - 7. As a second application we verify that there are only finitely many families of Calabi-Yau complete intersections of fixed dimension that are associated to a smooth Gorenstein polytope via the Batyrev-Borisov construction.
Place, publisher, year, edition, pages
2015. Vol. 67, no 4, 513-530 p.
Gorenstein polytopes, smooth reflexive polytopes, toric varieties, Fano manifolds, Calabi-Yau manifolds
IdentifiersURN: urn:nbn:se:su:diva-127068ISI: 000370395500004OAI: oai:DiVA.org:su-127068DiVA: diva2:905914