On Fano Varieties with Torus Action of Complexity 1

Abstract

AbstractIn this work we provide effective bounds and classification results for rational ℚ-factorial Fano varieties with a complexity-one torus action and Picard number 1 depending on the two invariants dimension and Picard index. This complements earlier work by Hausenet al., where the case of a free divisor class group of rank 1 was treated.