ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

4. Algebraic Geometry

1991 MS Classification: 14 Hausen, Jürgen, Universität Konstanz, Germany Toric Quotients Let H be a subtorus of the big torus of a toric variety X. The following result, presented in a joint work with A. A’Campo–Neuen (Konstanz) will be discussed: The action of H on X admits a toric quotient, i. e., there exists an H–invariant toric morphism p: X → Y that is universal with respect to H-invariant toric morphisms f: X → Z. Relations to other notions of quotients for the action of H on X will be given and generalizations to the category of toric prevarieties will be considered. Reference: A. A’Campo–Neuen and J. Hausen, Quotients of Toric Varieties by the Action of a Subtorus. To appear in Tohoku Math. J. .