×

Lifting of morphisms to quotient presentations. (English) Zbl 1014.14026

Summary: In this article we investigate algebraic morphisms between toric varieties. Given presentations of toric varieties as quotients we are interested in the question when a morphism admits a lifting to these quotient presentations. We show that this can be completely answered in terms of invariant divisors. As an application we prove that two toric varieties, which are isomorphic as abstract algebraic varieties, are even isomorphic as toric varieties. This generalizes a well-known result of A. S. Demushkin [Mosc. Univ. Math. Bull. 37, 104-111 (1982; Zbl 0507.14033)] on affine toric varieties.

MSC:

14M25 Toric varieties, Newton polyhedra, Okounkov bodies
14A10 Varieties and morphisms
14L30 Group actions on varieties or schemes (quotients)

Citations:

Zbl 0507.14033