The Index of a 1-Form on a Real Quotient Singularity

2018 ◽  
Vol 52 (2) ◽  
pp. 144-146
Author(s):  
S. M. Gusein-Zade ◽  
W. Ebeling
Keyword(s):  
Quotient Singularity

scholarly journals An algebraic formula for the index of a ‐form on a real quotient singularity

2018 ◽  
Vol 291 (17-18) ◽  
pp. 2543-2556
Author(s):  
Wolfgang Ebeling ◽  
Sabir M. Gusein‐Zade
Keyword(s):  
Quotient Singularity ◽  
Algebraic Formula

scholarly journals A software package for Mori dream spaces

2015 ◽  
Vol 18 (1) ◽  
pp. 647-659 ◽  
Author(s):  
Jürgen Hausen ◽  
Simon Keicher
Keyword(s):  
Software Package ◽  
Toric Varieties ◽  
Quotient Singularity ◽  
Algebraic Varieties ◽  
Cox Rings ◽  
Cox Ring ◽  
Mori Dream Spaces ◽  
The Common ◽  
Symplectic Resolutions

Mori dream spaces form a large example class of algebraic varieties, comprising the well-known toric varieties. We provide a first software package for the explicit treatment of Mori dream spaces and demonstrate its use by presenting basic sample computations. The software package is accompanied by a Cox ring database which delivers defining data for Cox rings and Mori dream spaces in a suitable format. As an application of the package, we determine the common Cox ring for the symplectic resolutions of a certain quotient singularity investigated by Bellamy–Schedler and Donten-Bury–Wiśniewski.

scholarly journals On the Grothendieck group of a quotient singularity defined by a finite abelian group

1992 ◽  
Vol 149 (1) ◽  
pp. 122-138 ◽  
Author(s):  
Jürgen Herzog ◽  
Eduardo Marcos ◽  
Rolf Waldi
Keyword(s):  
Abelian Group ◽  
Finite Abelian Group ◽  
Grothendieck Group ◽  
Quotient Singularity

scholarly journals Generating sequences and semigroups of valuations on 2 dimensional normal local rings

2018 ◽  
Author(s):  
◽  
Arpan Dutta
Keyword(s):  
Abelian Group ◽  
Finite Abelian Group ◽  
Local Rings ◽  
Closed Field ◽  
Quotient Singularity ◽  
Two Dimensional ◽  
Invariant Ring ◽  
Rational Rank ◽  
Generating Sequence ◽  
Generating Sequences

In this thesis we develop a method for constructing generating sequences for valuations dominating the ring of a two dimensional quotient singularity. Suppose that K is an algebraically closed field of characteristic zero, K[X, Y] is a polynomial ring over K and v is a rational rank 1 valuation of the field K(X, Y) which dominates K[X, Y](X,Y) . Given a finite Abelian group H acting diagonally on K[X, Y], and a generating sequence of v in K[X, Y] whose members are eigenfunctions for the action of H, we compute a generating sequence for the invariant ring K[X, Y]H. We use this to compute the semigroup SK[X,Y ]H (v) of values of elements of K[X, Y]H. We further determine when SK[X,Y ]H (v) is a finitely generated SK[X,Y ]H (v)-module.

Functions on quotient singularities

1987 ◽  
Vol 324 (1576) ◽  
pp. 1-45 ◽  
Keyword(s):  
Invariant Theory ◽  
Quotient Singularity ◽  
Two Dimensional ◽  
Comprehensive Review ◽  
Invariant Functions ◽  
Quotient Singularities ◽  
Free Actions

There are two main results: a determination of the modality of a generic function on any given two-dimensional quotient singularity and a listing of all the zero-modal functions. To achieve this, a comprehensive review of the invariant theory for free actions on C 2 is needed. The problem is put in context by a general discussion of classification of invariant functions, and several different extensions of the main results are indicated.

scholarly journals On the Classification of ALE Kähler Manifolds

2020 ◽  
Author(s):  
Hans-Joachim Hein ◽  
Rareş Răsdeaconu ◽  
Ioana Şuvaina
Keyword(s):  
Complex Structure ◽  
Kähler Manifold ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Quotient Singularity ◽  
Kahler Manifold ◽  
Kähler Surfaces

Abstract The underlying complex structure of an ALE Kähler manifold is exhibited as a resolution of a deformation of an isolated quotient singularity. As a consequence, there exist only finitely many diffeomorphism types of minimal ALE Kähler surfaces with a given group at infinity.

scholarly journals COX RINGS OF MINIMAL RESOLUTIONS OF SURFACE QUOTIENT SINGULARITIES

2015 ◽  
Vol 58 (2) ◽  
pp. 325-355 ◽  
Author(s):  
MARIA DONTEN-BURY
Keyword(s):  
Toric Variety ◽  
Affine Space ◽  
Explicit Description ◽  
Quotient Singularity ◽  
Coordinate Ring ◽  
Minimal Resolution ◽  
Cox Rings ◽  
Cox Ring ◽  
Quotient Singularities ◽  
Minimal Resolutions

AbstractWe investigate Cox rings of minimal resolutions of surface quotient singularities and provide two descriptions of these rings. The first one is the equation for the spectrum of a Cox ring, which is a hypersurface in an affine space. The second is the set of generators of the Cox ring viewed as a subring of the coordinate ring of a product of a torus and another surface quotient singularity. In addition, we obtain an explicit description of the minimal resolution as a divisor in a toric variety.

scholarly journals Orbifolds and finite group representations

2001 ◽  
Vol 26 (11) ◽  
pp. 649-669
Author(s):  
Li Chiang ◽  
Shi-Shyr Roan
Keyword(s):  
Finite Group ◽  
Abelian Group ◽  
Representation Theory ◽  
Hilbert Scheme ◽  
Group Representation ◽  
Quotient Singularity ◽  
Group Representations ◽  
Group Representation Theory ◽  
Crepant Resolutions

We present our recent understanding on resolutions of Gorenstein orbifolds, which involves the finite group representation theory. We concern only the quotient singularity of hypersurface type. The abelian groupAr(n)forA-type hypersurface quotient singularity of dimensionnis introduced. Forn=4, the structure of Hilbert scheme of group orbits and crepant resolutions ofAr(4)-singularity are obtained. The flop procedure of4-folds is explicitly constructed through the process.

scholarly journals A homology plane of general type can have at most a cyclic quotient singularity

2013 ◽  
Vol 23 (1) ◽  
pp. 1-62 ◽  
Author(s):  
R. V. Gurjar ◽  
M. Koras ◽  
M. Miyanishi ◽  
P. Russell
Keyword(s):  
General Type ◽  
Quotient Singularity ◽  
Cyclic Quotient Singularity

scholarly journals Counting resolutions of symplectic quotient singularities

2015 ◽  
Vol 152 (1) ◽  
pp. 99-114 ◽  
Author(s):  
Gwyn Bellamy
Keyword(s):  
Simple Formula ◽  
Finite Subgroup ◽  
Quotient Singularity ◽  
Symplectic Resolution ◽  
Quotient Singularities ◽  
Symplectic Resolutions

Let ${\rm\Gamma}$ be a finite subgroup of $\text{Sp}(V)$. In this article we count the number of symplectic resolutions admitted by the quotient singularity $V/{\rm\Gamma}$. Our approach is to compare the universal Poisson deformation of the symplectic quotient singularity with the deformation given by the Calogero–Moser space. In this way, we give a simple formula for the number of $\mathbb{Q}$-factorial terminalizations admitted by the symplectic quotient singularity in terms of the dimension of a certain Orlik–Solomon algebra naturally associated to the Calogero–Moser deformation. This dimension is explicitly calculated for all groups ${\rm\Gamma}$ for which it is known that $V/{\rm\Gamma}$ admits a symplectic resolution. As a consequence of our results, we confirm a conjecture of Ginzburg and Kaledin.

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