Change search
ReferencesLink to record
Permanent link

Direct link
On smooth Gorenstein polytopes
Stockholm University, Faculty of Science, Department of Mathematics.
2015 (English)In: Tohoku mathematical journal, ISSN 0040-8735, Vol. 67, no 4, 513-530 p.Article in journal (Refereed) Published
Abstract [en]

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.
Keyword [en]
Gorenstein polytopes, smooth reflexive polytopes, toric varieties, Fano manifolds, Calabi-Yau manifolds
National Category
Discrete Mathematics
Identifiers
URN: urn:nbn:se:su:diva-127068ISI: 000370395500004OAI: oai:DiVA.org:su-127068DiVA: diva2:905914
Available from: 2016-02-23 Created: 2016-02-23 Last updated: 2016-03-14Bibliographically approved

Open Access in DiVA

No full text

Search in DiVA

By author/editor
Nill, Benjamin
By organisation
Department of Mathematics
In the same journal
Tohoku mathematical journal
Discrete Mathematics

Search outside of DiVA

GoogleGoogle Scholar
The number of downloads is the sum of all downloads of full texts. It may include eg previous versions that are now no longer available

Total: 22 hits
ReferencesLink to record
Permanent link

Direct link