Canonical divisors on T-varieties

2008/11/05 by Hendrik Süß, Süß, Hendrik · 3 citations
Mathematics · #14C20 #14J45 #14L30 #52B20 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.0811.0626

openalex publication_date 2008/11/05 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28

Abstract

Generalising toric geometry we study compact varieties admitting lower dimensional torus actions. In particular we describe divisors on them in terms of convex geometry and give a criterion for their ampleness. These results may be used to study Fano varieties with small torus actions. As a first result we classify log del Pezzo C*-surfaces of Picard number 1 and Gorenstein index less than 4. In further examples we show how classification might work in higher dimensions and we give explicit descriptions of some equivariant smoothings of Fano threefolds.

Citations

• Dual Polyhedra and Mirror Symmetry for Calabi-Yau Hypersurfaces in Toric Varieties

Cited by

• Okounkov Bodies of Complexity-One T-Varieties
• Euler sequence for complete smooth k*-surfaces
• On Fano varieties with torus action of complexity one

Related

• Toric Fano varieties with divisorial contractions to curves
• Toric varieties whose canonical divisors are divisible by their dimensions
• Toric Degenerations of Fano Varieties and Constructing Mirror Manifolds
• Toric Fano varieties and birational morphisms
• Toric varieties whose blow-up at a point is Fano