• Corpus ID: 242757218

Reductive quotients of klt singularities

  title={Reductive quotients of klt singularities},
  author={Lukas Braun and Daniel Greb and Kevin Langlois and Joaqu'in 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 quasiprojective good quotient X Ñ X{{G, we can find a boundary B on X{{G so that the pair pX{{G,Bq 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… 

Reductive covers of klt varieties

. 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 P GL n p K q -cover that is not of klt type. Then,

On automorphisms of semistable G-bundles with decorations

We prove a rigidity result for automorphisms of points of certain stacks admitting adequate moduli spaces. It encompasses as special cases variations of the moduli of G -bundles on a smooth

Non-isomorphic smooth compactifications of the moduli space of cubic surfaces

A BSTRACT . The well-studied moduli space of complex cubic surfaces has three different, but isomorphic, compact realizations: as a GIT quotient M GIT , as a Baily–Borel compactification of a ball

On the boundedness of singularities via normalized volume

. In this article we study conjectures regarding normalized volume and boundedness of singularities. We focus on hypersurface singularities and singularities with a torus action of complexity one.

Pure subrings of Du Bois singularities are Du Bois singularities

. Let R → S be a cyclically pure map of rings essentially of finite type over the complex numbers C . In this paper, we show that if S has Du Bois singularities, then R has Du Bois singularities. Our

Coregularity of Fano varieties

. The regularity of a Fano variety, denoted by reg p X q , is the largest dimension of the dual complex of a log Calabi–Yau structure on X . The coregularity is defined to be coreg p X q : “ dim X ´

Deformations of log terminal and semi log canonical singularities

. In this paper, we prove that klt singularities are invariant under deformations if the generic fiber is Q -Gorenstein. We also obtain a similar result for slc singularities. These are

Singularities of determinantal pairs

. Let X be a generic determinantal affine variety over a perfect field of characteristic p ≥ 0 and P ⊂ X be a standard prime divisor generator of Cl X ∼ = Z . We prove that the pair ( X, P ) is purely F



Analytic Hilbert Quotients

We give a systematic treatment of the quotient theory for a holomorphic action of a reductive group G = K on a not necessarily compact Kählerian space X. This is carried out via the complex geometry

Mori dream spaces and GIT.

The main goal of this paper is to study varieties with the best possible Mori theoretic properties (measured by the existence of a certain decomposition of the cone of effective divisors). We call

On the collapsing of homogeneous bundles in arbitrary characteristic

We study the geometry of equivariant, proper maps from homogeneous bundles G×P V over flag varieties G/P to representations of G, called collapsing maps. Kempf showed that, provided the bundle is

Log-terminal singularities and vanishing theorems via non-standard tight closure

Generalizing work of Smith and Hara, we give a new characterization of logterminal singularities for finitely generated algebras over C, in terms of purity properties of ultraproducts of


Firstly, we see that the bases of the miniversal deformations of isolated Q-Gorenstein toric singularities are quite restricted. In particular, we classify the analytic germs of embedding dimension ≤

Globally F-regular varieties: applications to vanishing theorems for quotients of Fano varieties.

H (X, (L ⊗ ω−1) ⊗ ω) vanishes whenL ⊗ ω−1 is ample, and hence vanishing holds in particular whenever L is numerically effective andω−1 is ample. In this paper, a class of algebraic varieties is

Complex-analytic quotients of algebraic $$G$$G-varieties

It is shown that any compact semistable quotient of a normal variety by a complex reductive Lie group $$G$$G (in the sense of Heinzner and Snow) is a good quotient. This reduces the investigation and


IN this paper, we present a framework for studying moduli spaces of finite dimensional representations of an arbitrary finite dimensional algebra A over an algebraically closed field k. (The abelian

Fundamental groups of links of isolated singularities

© 2014 American Mathematical Society. All rights reserved. We study fundamental groups of projective varieties with normal crossing singularities and of germs of complex singularities. We prove that

Rational , Log Canonical , Du Bois Singularities II : Kodaira Vanishing and Small Deformations *

Kollär's conjecture, that log canonical singularities areDuBois, is proved in the case of Cohen^Macaulay 3-folds. This in turn is used to derive Kodaira vanishing for this class of varieties. Finally