Geometry of Hilbert Quotients and Hilbert Families
Prof. Yi Hu
2023-07-07 10:30-11:30
MCM110
Speaker: Prof. Yi Hu (The University of Arizona)Time: 10:30-11:30 July 7, 2023 (Friday)
Place: MCM110
Title: Geometry of Hilbert Quotients and Hilbert Families
Abstract: Given a reductive group acting on a projective variety, there exists the canonical Hilbert quotient, parameterizing the closures of general orbits and their degenerations. Motivated by Lafforgue's version of Mnev's Universality, which we will review in the talk, we investigate the Hilbert quotient and Hilbert family of Grassmannian Gr(d,n) by the maximal torus. When d=2, the Hilbert quotient of Gr(2,n) is the moduli of Deligne-Mumford stable rational curves with n marked points; when d=3, the Hilbert quotient is the main component of the muduli of pairs (P^2, H_1+...+ H_n), where H_i are distinct lines on P^2, and their KSBA-degenerations. Except the above, little is known about the Hilbert quotient of Gr(d,n). We will discuss my recent results on the canonical embeddings of the Hilbert quotient and Hilbert family of Gr(d,n) into certain products of projective spaces and their explicit defining equations.
