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My preprints on arXiv. My published papers on MathSciNet (subscription required). My Google Scholar entry.

Publications

PREPRINTS

• Reductive quotients of klt singularities, arXiv:2111.02812
(with Lukas Braun, Kevin Langlois, and Joaquín Moraga)

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. Our main result has consequences for complex spaces obtained as quotients of Hamiltonian Kähler $G$-manifolds, for collapsings of homogeneous vector bundles as introduced by Kempf, 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. As a corresponding result regarding global geometry, we show that quotients of Mori Dream Spaces with klt Cox rings are Mori Dream Spaces with klt Cox ring. This in turn applies to show that projective GIT-quotients of varieties of Fano type are of Fano type; in particular, projective moduli spaces of semistable quiver representations are of Fano type.

• 1-rational singularities and quotients by reductive groups, arXiv:0901.3539

This preprint will not be submitted; the results follow easily from those in my later paper ''Rational singularities and quotients by holomorphic group actions'' that appeared in Annali della Scuola Normale Superiore di Pisa; however, the preprint gives an independent and technically simpler proof in the algebraic case and avoids the technical difficulties encountered in the analytic setup.

MathSciNet-Reviews

Reviews written by myself for Mathematical Reviews can be found here (subscription required).