Seminar Algebra and Geometry: Ivan Bazhov (Univesité de Genève)

On orbits of the automorphism group on an affine toric variety

Let X be an affine toric variety and Aut(X) be its automorphism group. In the first part of the talk we give a combinatorial description of Aut(X)-orbits on X in terms of the divisor class group Cl(X).
In the second part we introduce the total coordinates on X. The total coordinate ring provides a canonical presentation $\overline{X}$ → X of X as a quotient of a vector space $\overline{X}$ by a linear action of a quasitorus. We show that the orbits of the connected component of the group Aut(X) on X coincide with the Luna strata defined by the canonical quotient presentation.

Veranstaltung übernehmen als iCal