Algebraic and Arithmetic Geometry Seminar

Degenerations of Hilbert schemes and relative VGIT

by Lars Halvard Halle (Università di Bologna)

Aula Magna (Department of Mathematics)

Aula Magna

Department of Mathematics

Let G be a reductive group acting on a projective variety X.  In Mumford's Geometric Invariant Theory (GIT),  the formation of a quotient in this situation depends on the choice of a G-linearized ample line bundle on X. In "Variation of GIT" (VGIT), one studies various aspects of this dependence. 

I will report on joint work with K. Hulek and Z. Zhang, and explain how some central results in VGIT can be extended to a relative setting. Our main motivation was to apply these results to the study of certain Hilbert scheme degenerations constructed as relative GIT quotients. In the second part of the talk, I will indicate how VGIT can be used to provide a conceptual understanding of the (semi)stable locus in this quotient construction.