## Geometry Seminar - Abstracts

### Talk

Wednesday 29 March 2023, 16:00 - 17:00 in HG03.085

**Dominic Bunnett** (TU Berlin)

*Moduli spaces of weighted hypersurfaces*

### Abstract

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.

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