Change search
ReferencesLink to record
Permanent link

Direct link
Polyhedral adjunction theory
KTH, School of Engineering Sciences (SCI), Mathematics (Dept.), Mathematics (Div.).ORCID iD: 0000-0002-7186-1524
2013 (English)In: Algebra & Number Theory, ISSN 1937-0652, Vol. 7, no 10, 2417-2446 p.Article in journal (Refereed) Published
Abstract [en]

In this paper we offer a combinatorial view on the adjunction theory of toric varieties. Inspired by classical adjunction theory of polarized algebraic varieties we explore two convex-geometric notions: the Q-codegree and the nef value of a rational polytope P. We prove a structure theorem for lattice polytopes P with large Q-codegree. For this, we define the adjoint polytope P-(s) as the set of those points in P whose lattice distance to every facet of P is at least s. It follows from our main result that if P-(s) is empty for some s < 2/(dim P + 2), then the lattice polytope P has lattice width one. This has consequences in Ehrhart theory and on polarized toric varieties with dual defect. Moreover, we illustrate how classification results in adjunction theory can be translated into new classification results for lattice polytopes.

Place, publisher, year, edition, pages
2013. Vol. 7, no 10, 2417-2446 p.
Keyword [en]
convex polytopes, toric varieties, adjunction theory
National Category
URN: urn:nbn:se:kth:diva-145790DOI: 10.2140/ant.2013.7.2417ISI: 000335456500002ScopusID: 2-s2.0-84898817806OAI: diva2:721135

QC 20140603

Available from: 2014-06-03 Created: 2014-06-02 Last updated: 2014-06-03Bibliographically approved

Open Access in DiVA

No full text

Other links

Publisher's full textScopus

Search in DiVA

By author/editor
Di Rocco, Sandra
By organisation
Mathematics (Div.)
In the same journal
Algebra & Number Theory

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

Altmetric score

Total: 36 hits
ReferencesLink to record
Permanent link

Direct link