# Moment maps for non-reductive group actions in Kähler geometry

### Frances Kirwan (Oxford)

09-Dec-2021, 16:15-17:15 (14 months ago)

Abstract: When a complex reductive group $G$ acts linearly on a projective variety $X$, the GIT quotient $X//G$ can be identified with a symplectic quotient of $X$ by a Hamiltonian action of a maximal compact subgroup $K$ of $G$. Here the moment map takes values in the (real) dual of the Lie algebra of $K$, which embeds naturally in the complex dual of the Lie algebra of $G$ (as those complex linear maps taking real values on $\mathfrak{k}$). The aim of this talk is to discuss an analogue of this description for GIT quotients by suitable non-reductive actions, where the analogue of the moment map takes values in the complex dual of the Lie algebra of the non-reductive group. This is joint work with Gergely Berczi.

mathematical physicsalgebraic geometrydifferential geometryrepresentation theorysymplectic geometry

Audience: researchers in the topic