Quotient Singularities and Their Resolutions

1986 ◽  
pp. 118-176
Author(s):  
Klaus Lamotke
Keyword(s):  
Quotient Singularities

scholarly journals The Kodaira Problem for Kähler Spaces with Vanishing First Chern Class

2021 ◽  
Vol 9 ◽  
Author(s):  
Patrick Graf ◽  
Martin Schwald
Keyword(s):  
Chern Class ◽  
Cohomology Group ◽  
Canonical Bundle ◽  
Deformation Space ◽  
Projective Varieties ◽  
Quotient Singularities ◽  
Finite Quotient ◽  
First Chern Class ◽  
Small Deformations

Abstract Let X be a normal compact Kähler space with klt singularities and torsion canonical bundle. We show that X admits arbitrarily small deformations that are projective varieties if its locally trivial deformation space is smooth. We then prove that this unobstructedness assumption holds in at least three cases: if X has toroidal singularities, if X has finite quotient singularities and if the cohomology group ${\mathrm {H}^{2} \!\left ( X, {\mathscr {T}_{X}} \right )}$ vanishes.

scholarly journals On the Fundamental Group of a Variety with Quotient Singularities

2013 ◽  
Vol 2015 (5) ◽  
pp. 1421-1444 ◽  
Author(s):  
Indranil Biswas ◽  
Amit Hogadi
Keyword(s):  
Fundamental Group ◽  
Quotient Singularities

scholarly journals EQUIVARIANT HIRZEBRUCH CLASSES AND MOLIEN SERIES OF QUOTIENT SINGULARITIES

2017 ◽  
Vol 23 (3) ◽  
pp. 671-705 ◽  
Author(s):  
MARIA DONTEN-BURY ◽  
ANDRZEJ WEBER
Keyword(s):  
Quotient Singularities ◽  
Molien Series

scholarly journals Asymptotically conical Calabi-Yau metrics with cone singularities along a compact divisor

2019 ◽  
Author(s):  
Martin de Borbon ◽  
Cristiano Spotti
Keyword(s):  
Finite Subgroup ◽  
Minimal Resolution ◽  
Gravitational Instantons ◽  
Normal Crossing ◽  
Three Sphere ◽  
Asymptotically Locally Euclidean ◽  
Quotient Singularities ◽  
Simple Normal Crossing

Abstract We construct Asymptotically Locally Euclidean (ALE) and, more generally, asymptotically conical Calabi–Yau metrics with cone singularities along a compact simple normal crossing divisor. In particular, this includes the case of the minimal resolution of 2D quotient singularities for any finite subgroup $\Gamma \subset U(2)$ acting freely on the three-sphere, hence generalizing Kronheimer’s construction of smooth ALE gravitational instantons.

Wild quotient singularities of surfaces

2013 ◽  
Vol 275 (1-2) ◽  
pp. 211-232 ◽  
Author(s):  
Dino Lorenzini
Keyword(s):  
Quotient Singularities

scholarly journals Derived categories of resolutions of cyclic quotient singularities

2017 ◽  
Vol 69 (2) ◽  
pp. 509-548 ◽  
Author(s):  
Andreas Krug ◽  
David Ploog ◽  
Pawel Sosna
Keyword(s):  
Derived Categories ◽  
Quotient Singularities ◽  
Cyclic Quotient Singularities

A Non-vanishing Theorem of Del Pezzo Surfaces

2016 ◽  
Vol 59 (2) ◽  
pp. 463-472
Author(s):  
Chin-Yi Lin
Keyword(s):  
Del Pezzo Surfaces ◽  
Vanishing Theorem ◽  
Quotient Singularities ◽  
Del Pezzo

AbstractWe develop a new non-vanishing theorem for del Pezzo surfaces with quotient singularities.

scholarly journals Nonrational Weighted Hypersurfaces

2009 ◽  
Vol 194 ◽  
pp. 1-32 ◽  
Author(s):  
Takuzo Okada
Keyword(s):  
Arbitrary Dimension ◽  
Fano Varieties ◽  
Fano Threefolds ◽  
Alternate Proof ◽  
Quotient Singularities

AbstractThe aim of this paper is to construct (i) infinitely many families of nonrational ℚ-Fano varieties of arbitrary dimension ≥ 4 with at most quotient singularities, and (ii) twelve families of nonrational ℚ-Fano threefolds with at most terminal singularities among which two are new and the remaining ten give an alternate proof of nonrationality to known examples. These are constructed as weighted hypersurfaces with the reduction mod p method introduced by Kollár [10].

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