Variation of Stratifications in Invariant Theory

Thursday, October 8, 2020 - 2:00pm
Chi-yu Cheng

Mumford's Geometric Invariant Theory was developed to construct quotients in algebraic geometry. The unstable points are discarded to obtain a better quotient. However, the unstable locus has interesting stories. In this talk, I will introduce a stratification on the unstable locus in the affine setting; provide examples and results on variations of stratifications from Cox's GIT quotient construction of projective toric varieties;
how the variation is captured by certain kinds of closed subsets in the space of characters of the group acting on the affine variety in general.

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