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- W4307005802 abstract "In this article, we study $G$-covers of klt varieties, where $G$ is a reductive group. First, we exhibit an example of a klt singularity admitting a $mathbb{P}{rm GL}_n(mathbb{K})$-cover that is not of klt type. Then, we restrict ourselves to $G$-quasi-torsors, a special class of $G$-covers that behave like $G$-torsors outside closed subsets of codimension two. Given a $G$-quasi-torsor $Xrightarrow Y$, where $G$ is a finite extension of a torus $mathbb{T}$, we show that $X$ is of klt type if and only if $Y$ is of klt type. We prove a structural theorem for $mathbb{T}$-quasi-torsors over normal varieties in terms of Cox rings. As an application, we show that every sequence of $mathbb{T}$-quasi-torsors over a variety with klt type singularities is eventually a sequence of $mathbb{T}$-torsors. This is the torus version of a result due to Greb-Kebekus-Peternell regarding finite quasi-torsors of varieties with klt type singularities. On the contrary, we show that in any dimension there exists a sequence of finite quasi-torsors and $mathbb{T}$-quasi-torsors over a klt type variety, such that infinitely many of them are not torsors. We show that every variety with klt type singularities is a quotient of a variety with canonical factorial singularities. We prove that a variety with Zariski locally toric singularities is indeed the quotient of a smooth variety by a solvable group. Finally, motivated by the work of Stibitz, we study the optimal class of singularities for which the previous results hold." @default.
- W4307005802 created "2022-10-22" @default.
- W4307005802 creator A5034128863 @default.
- W4307005802 creator A5075600941 @default.
- W4307005802 date "2022-10-18" @default.
- W4307005802 modified "2023-10-18" @default.
- W4307005802 title "Reductive covers of klt varieties" @default.
- W4307005802 doi "https://doi.org/10.48550/arxiv.2210.10095" @default.
- W4307005802 hasPublicationYear "2022" @default.
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