## Variations of GIT-quotients of flag varieties, ICMS Seminar Talk by Valdemar Tsanov

In this talk, partly based on joint work with H. Seppanen, I will present a description of the GIT-classes of L-ample line bundles on X and some properties of the respective GIT-quotients. Under mild assumptions, we prove the existence of a quotient whose Cox ring is, up to a finite extension, isomorphic to the ring of L-invariants in the Cox ring of X. This is indeed a special property, as such a quotient inherits, a priori, only information about the ample line bundle with respect to which it is defined.