Canonical divisors on T-varieties

Understand

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.