Change search
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf
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, E-ISSN 1944-7833, Vol. 7, no 10, p. 2417-2446Article 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, p. 2417-2446
Keywords [en]
convex polytopes, toric varieties, adjunction theory
National Category
Mathematics
Identifiers
URN: urn:nbn:se:kth:diva-145790DOI: 10.2140/ant.2013.7.2417ISI: 000335456500002Scopus ID: 2-s2.0-84898817806OAI: oai:DiVA.org:kth-145790DiVA, id: diva2:721135
Note

QC 20140603

Available from: 2014-06-03 Created: 2014-06-02 Last updated: 2017-12-05Bibliographically approved

Open Access in DiVA

No full text in DiVA

Other links

Publisher's full textScopus

Authority records BETA

Di Rocco, Sandra

Search in DiVA

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

Search outside of DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric score

doi
urn-nbn
Total: 63 hits
CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf