On the combinatorial classification of toric log del Pezzo surfaces

DOI10.1112/S1461157008000387zbMath1230.14077arXiv0810.2207OpenAlexW3106473208MaRDI QIDQ3091987

Benjamin Nill, Maximilian Kreuzer, Alexander M. Kasprzyk

Publication date: 15 September 2011

Published in: LMS Journal of Computation and Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0810.2207

Mathematics Subject Classification ID

Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Rational and ruled surfaces (14J26) Toric varieties, Newton polyhedra, Okounkov bodies (14M25)

Related Items

On Fano Varieties with Torus Action of Complexity 1, On Barycentric transformations of Fano polytopes, Del Pezzo surfaces with a single \(1/k(1,1)\) singularity, Classification of toric log del Pezzo surfaces with few singular points, Unnamed Item, MINIMALITY AND MUTATION-EQUIVALENCE OF POLYGONS, Toric log del Pezzo surfaces with one singularity, Chern-Simons: Fano and Calabi-Yau, Stringy -functions of canonical toric Fano threefolds and their applications, On the twelve-point theorem for \(\ell\)-reflexive polygons, Classification of minimal polygons with specified singularity content, On deformations of toric Fano varieties, Finitely many smooth \(d\)-polytopes with \(n\) lattice points

Uses Software

• Graded Ring Database

Cites Work

• Complete classification of reflexive polyhedra in four dimensions
• Lectures on torus embeddings and applications. (Based on joint work with Katsuya Miyake.)
• Classification of reflexive polyhedra in three dimensions
• Rank one log del Pezzo surfaces of index two
• Introduction to Toric Varieties. (AM-131)
• Bounds for Lattice Polytopes Containing a Fixed Number of Interior Points in a Sublattice
• Lattice points in lattice polytopes