Moduli spaces of hypersurfaces and their topology

Abstract: A hypersurface is defined by the vanishing of a single polynomial equation. One constructs a moduli space of hypersurfaces by considering all equations and quotienting out by the group action given by changing coordinates. In the classical setting of hypersurfaces in projective space the group of coordinate changes is SLn which is a reductive group. Thus techniques of geometric invariant theory can be used to define notions of stability for hypersurfaces, put algebraic structure on the quotient space and even explicitly study the topology. In this talk, we revisit these classical techniques and extend them to the non-reductive setting, which is the setting for many moduli problems. We will compute the cohomology of the moduli spaces of some low degree del Pezzo surfaces.

Mathematics

Audience: researchers in the discipline

Comments: Room: STEM 3.1 findyourway.essex.ac.uk/bcdc98e0-e3c3-11eb-b52e-05a67b7792fc/search/projects/23/60ef1a882031e800c230405d

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MESS (Mathematics Essex Seminar Series)

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