Families of Invariant Divisors on Rational Complexity-One T-Varieties

Abstract

We study invariant divisors on the total spaces of the homogeneous deformations of rational complexity-one T-varieties constructed by Ilten and Vollmert. In particular, we identify a natural subgroup of the Picard group for any general fiber of such a deformation, which is canonically isomorphic to the Picard group of the special fiber. This isomorphism preserves Euler characteristic, intersection numbers, and the canonical class.

v4 minor changes: 17 pages and 3 figures

References in corpus (3)

• Examples for exceptional sequences of invertible sheaves on rational surfaces
• Upgrading and Downgrading Torus Actions
• Exceptional Sequences on Rational C*-Surfaces

Cited by in corpus (6)

• On Generalized Wronskians
• The Geometry of T-Varieties
• Exceptional Sequences on Rational C*-Surfaces
• On deformation spaces of toric singularities and on singularities of K-moduli of Fano varieties
• Homogeneous deformations of toric pairs
• DG categories and exceptional collections