Back to Commutative Algebra Seminar: Spring 2018
Commutative Algebra Seminar
Date: Friday, Jan 19, 2018
Time: 2:30PM - 3:20PM
Location: LCB 222
Hans-Christian Herbig
CEP, Brazil
Title |
Moment map phenomenology |
Abstract |
In the study of quadratic moment maps there appears to be a dichotomy between large and small representations. In the large case the moment map exhibits some features of regularity. This enables one to make qualitative and quantitative statements about the symplectic quotients. In the talk I will report on recent joint work with Gerald Schwarz and Christopher Seaton which proves that for 2-large representations the appropriately defined complex symplectic quotient has symplectic singularities. This in particular entails that the symplectic quotient is graded Gorenstein domain and is a normal variety with rational singularities. Furthermore, using a recent theorem of of P. Etingof and T. Schedler, it follows as a corollary that in the 2-large case the space of Poisson traces is finite dimensional. It is expected that the result generalizes to small representations as well, even though here the moment map can have all sorts of pathologies. For this conjecture it is crucial to use the definition of the symplectic quotient that involves the real radical of the ideal generated by the moment map. |
Commutative Algebra