Prof. Dr. Daniel Greb - Publications


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



  • 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. Furthermore, our result has implications for complex spaces obtained as momentum map quotients of Hamiltonian Kähler 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.

  • 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.


CONFERENCE PROCEEDINGS (invited, without peer review)




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