Deformations of Rational T-Varieties

Abstract

We show how to construct certain homogeneous deformations for rational normal varieties with codimension one torus action. This can then be used to construct homogeneous deformations of any toric variety in arbitrary degree. For locally trivial deformations coming from this construction, we calculate the image of the Kodaira-Spencer map. We then show that for a smooth complete toric variety, our homogeneous deformations span the space of first-order deformations.

22 pages, 9 figures; v2 minor changes to introduction; v3 some corrections, to appear in Journal of Algebraic Geometry

References in corpus (5)

• Normal singularities with torus actions
• Canonical divisors on T-varieties
• Deformations of Toric Varieties via Minkowski Sum Decompositions of Polyhedral Complexes
• Deformations of Smooth Toric Surfaces
• One-Parameter Toric Deformations of Cyclic Quotient Singularities

Cited by in corpus (13)

• K-Stability for Fano Manifolds with Torus Action of Complexity One
• Infinite transitivity on universal torsors
• Mutations of Laurent Polynomials and Flat Families with Toric Fibers
• Deformations of Toric Varieties via Minkowski Sum Decompositions of Polyhedral Complexes
• Upgrading and Downgrading Torus Actions
• Rational Complexity-One T-Varieties are Well-Poised
• Exceptional Sequences on Rational C*-Surfaces
• Families of Invariant Divisors on Rational Complexity-One T-Varieties
• Deformations of constant scalar curvature Sasakian metrics and K-stability
• On deformation spaces of toric singularities and on singularities of K-moduli of Fano varieties
• Homogeneous deformations of toric pairs
• Deformations of Smooth Complete Toric Varieties: Obstructions and the Cup Product
• Flexible affine cones and flexible coverings