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Seminar aimed at a general audience by Gergely Berczi (University of Oxford)

Title: Reductive versus non-reductive group actions and moduli spaces

2016.04.01 | Jane Jamshidi

Date Fri 08 Apr
Time 11:15 12:10
Location 1531-119 (Aud. D2)


Moduli spaces parametrize geometric objects up to certain symmetries. These symmetries are often manifested as group actions on parameter spaces and the moduli space parametrize orbits of this action and therefore we can think of it as the quotient of the parameter space by the symmetry group. Mumford's geometric invariant theory (GIT) provides a method for constructing (projective completions of) quotient varieties for linear actions of complex reductive groups on affine and projective varieties, and has become a fundamental approach in describing moduli spaces in algebraic geometry. Mumford's GIT can be extended to actions of linear algebraic groups which are not necessarily reductive, but many of the nice properties belonging to reductive GIT no longer hold for non-reductive actions. The aim of this talk is to give a gentle introduction to the basic features of reductive vs non-reductive algebraic group actions and to describe some conditions under which the good properties satisfied by reductive GIT still hold for suitable non-reductive actions. Much of the material beyond the classical results will be based on joint work with Frances Kirwan, Brent Doran and Tom Hawes.

NOTE: This seminar is aimed at a general audience of mathematicians.