Emmy-Noether-Seminar: Horospherical varieties with quotient singularities

Horospherical varieties with quotient singularities

Sean Monahan (München)

Abstract: Quotient singularities are defined as an étale-local property of varieties, but one can ask if this is actually a global property, possibly when restricted to a particular class of varieties. I am interested in addressing this for horospherical varieties, which are a generalization of toric varieties where one replaces the acting torus with any reductive group. To start, I will introduce these horospherical varieties and their known combinatorial theory via so-called coloured fans, which generalizes the toric theory using polyhedral fans. Then I will highlight my results: first, a combinatorial characterization of quotient singularities on these varieties; and second, a corollary that quotient singularities are indeed a global property in this case.