KASS seminar

Abstract: If X is a projective variety with an action of a reductive group G, Geometric Invariant Theory (GIT) yields a projective quotient of X by G. This construction depends on the choice of a G-linearised ample line bundle L on X.  Varying L, it is known that we obtain birational GIT quotients, but only finitely many varieties arise in this way. Borrowing from the theory of Zariski--Riemann spaces, we explain how to construct a "universal" GIT quotient capturing all possible varieties birational to a given GIT quotient. This is based on joint work with Ruadhaí Dervan.