Wednesday 29 March 2023, 16:00 - 17:00 in HG03.085
Dominic Bunnett (TU Berlin)
Moduli spaces of weighted hypersurfaces
The moduli space of smooth hypersurfaces of degree d in a projective space is constructed using geometric invariant theory (GIT) as the quotient by the action of the projective linear group on the space of degree d polynomials with the discriminant locus of singular polynomials removed. Moduli spaces of quasi-smooth hypersurfaces in weighted projective space can also be constructed as quotients of group actions using GIT; however, automorphism groups of weighted projective spaces are non-reductive and so new results of non-reductive geometric invariant theory (NRGIT) must be applied. In this talk, I'll introduce the moduli space of such hypersurfaces and notions of stability coming from NRGIT. I will also discuss the theory of discriminants describing the loci of quasi-smooth hypersurfaces. Time permitting, I will compare, for some specific cases, notions of NRGIT stability with K-stability and compute the cohomology of the corresponding moduli spaces.