Complete toric varieties with reductive automorphism group

DOI10.1007/s00209-005-0880-zzbMath1091.14011arXivmath/0407491OpenAlexW2037381940MaRDI QIDQ818781

Benjamin Nill

Publication date: 21 March 2006

Published in: Mathematische Zeitschrift (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/math/0407491

zbMATH Keywords

toric varietyFano varietyalgebraic grouplattice polytope

Mathematics Subject Classification ID

Lattice polytopes in convex geometry (including relations with commutative algebra and algebraic geometry) (52B20) Toric varieties, Newton polyhedra, Okounkov bodies (14M25) Fano varieties (14J45) Automorphisms of surfaces and higher-dimensional varieties (14J50)

Related Items (14)

The number of vertices of a Fano polytope ⋮ Root subgroups on affine spherical varieties ⋮ Twisted forms of toric varieties ⋮ On orbits of the automorphism group on a complete toric variety ⋮ Favourable modules: filtrations, polytopes, Newton-Okounkov bodies and flat degenerations ⋮ Additive group actions on affine \(\mathbb{T}\)-varieties of complexity one in arbitrary characteristic ⋮ Gale duality and homogeneous toric varieties ⋮ Lattices generated by skeletons of reflexive polytopes ⋮ A Calabi-Yau database: threefolds constructed from the Kreuzer-Skarke list ⋮ Examples of Kähler-Einstein toric Fano manifolds associated to non-symmetric reflexive polytopes ⋮ A polar dual to the momentum of toric Fano manifolds ⋮ Examples on Loewy filtrations and K-stability of Fano varieties with non-reductive automorphism groups ⋮ On toric geometry and K-stability of Fano varieties ⋮ Bounds on the Picard rank of toric Fano varieties with minimal curve constraints

Uses Software

• PALP

Cites Work

• PALP: a package for analysing lattice polytopes with applications to toric geometry
• Einstein-Kähler forms, Futaki invariants and convex geometry on toric Fano varieties
• Calabi-Yau 4-folds and toric fibrations
• Polytopal linear groups
• Gorenstein toric Fano varieties
• Polyhedral \(K_{2}\)
• Kähler--Ricci solitons on toric manifolds with positive first Chern class
• Introduction to Toric Varieties. (AM-131)
• Einstein-Kähler metrics on symmetric toric Fano manifolds
• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties
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