Author
Kevin Langlois
Bio: Kevin Langlois is an academic researcher. The author has contributed to research in topics: Reductive group & Quotient. The author has co-authored 1 publications.
Topics: Reductive group, Quotient, Moment map, Moduli space
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TL;DR: In this paper, it was shown that the quotient of a klt type singularity by a reductive group is of klt-type, which implies that the good moduli space parametrizing K-polystable Fano manifolds of volume $v$ has klt types.
Abstract: We prove that the quotient of a klt type singularity by a reductive group is of klt type. In particular, given a klt variety $X$ endowed with the action of a reductive group $G$ and admitting a quasi-projective good quotient $X\rightarrow X/\!/G$, we can find a boundary $B$ on $X/\!/G$ so that the pair $(X/\!/G,B)$ is klt. This applies for example to GIT-quotients of klt varieties. Furthermore, our result has implications for complex spaces obtained as momentum map quotients of Hamiltonian K\"ahler manifolds and for good moduli spaces of smooth Artin stacks. In particular, it implies that the good moduli space parametrizing $n$-dimensional K-polystable Fano manifolds of volume $v$ has klt type singularities.