The classification of quotient singularities which are complete intersections

1984 ◽  
pp. 102-120 ◽  
Author(s):  
Haruhisa Nakajima ◽  
Kei-ichi Watanabe
Keyword(s):  
Complete Intersections ◽  
Quotient Singularities

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 Towards the classification of symplectic linear quotient singularities admitting a symplectic resolution

2021 ◽  
Author(s):  
Gwyn Bellamy ◽  
Johannes Schmitt ◽  
Ulrich Thiel
Keyword(s):  
Infinite Series ◽  
Classification Problem ◽  
Resolution Of Singularities ◽  
Crepant Resolution ◽  
Exceptional Group ◽  
Exceptional Groups ◽  
The Past ◽  
Symplectic Resolution ◽  
Quotient Singularities

AbstractOver the past 2 decades, there has been much progress on the classification of symplectic linear quotient singularities V/G admitting a symplectic (equivalently, crepant) resolution of singularities. The classification is almost complete but there is an infinite series of groups in dimension 4—the symplectically primitive but complex imprimitive groups—and 10 exceptional groups up to dimension 10, for which it is still open. In this paper, we treat the remaining infinite series and prove that for all but possibly 39 cases there is no symplectic resolution. We thereby reduce the classification problem to finitely many open cases. We furthermore prove non-existence of a symplectic resolution for one exceptional group, leaving $$39+9=48$$ 39 + 9 = 48 open cases in total. We do not expect any of the remaining cases to admit a symplectic resolution.

scholarly journals Classification of free actions on complete intersections of four quadrics

2011 ◽  
Vol 15 (4) ◽  
pp. 973-990 ◽  
Author(s):  
Zheng Hua
Keyword(s):  
Complete Intersections ◽  
Free Actions

scholarly journals THREE-DIMENSIONAL ISOLATED QUOTIENT SINGULARITIES IN EVEN CHARACTERISTIC

2017 ◽  
Vol 60 (2) ◽  
pp. 435-445
Author(s):  
VLADIMIR SHCHIGOLEV ◽  
DMITRY STEPANOV
Keyword(s):  
Finite Group ◽  
Vector Space ◽  
Three Dimensional ◽  
Finite Subgroup ◽  
Two Dimensional ◽  
Dimensional Vector ◽  
Dimensional Vector Space ◽  
Quotient Singularities ◽  
Characteristic 2

AbstractThis paper is a complement to the work of the second author on modular quotient singularities in odd characteristic. Here, we prove that if V is a three-dimensional vector space over a field of characteristic 2 and G < GL(V) is a finite subgroup generated by pseudoreflections and possessing a two-dimensional invariant subspace W such that the restriction of G to W is isomorphic to the group SL2(𝔽2n), then the quotient V/G is non-singular. This, together with earlier known results on modular quotient singularities, implies first that a theorem of Kemper and Malle on irreducible groups generated by pseudoreflections generalizes to reducible groups in dimension three, and, second, that the classification of three-dimensional isolated singularities that are quotients of a vector space by a linear finite group reduces to Vincent's classification of non-modular isolated quotient singularities.

Gorenstein Isolated Quotient Singularities Over ℂ

2014 ◽  
Vol 57 (3) ◽  
pp. 811-839 ◽  
Author(s):  
D. A. Stepanov
Keyword(s):  
Complex Numbers ◽  
Quotient Singularities

AbstractIn this paper we review the classification of isolated quotient singularities over the field of complex numbers due to Zassenhaus, Vincent and Wolf. As an application, we describe Gorenstein isolated quotient singularities over ℂ, generalizing a result of Kurano and Nishi.

Topological classification of 4-dimensional complete intersections

1996 ◽  
Vol 90 (1) ◽  
pp. 139-147 ◽  
Author(s):  
Fang Fuquan ◽  
Stephan Klaus
Keyword(s):  
Topological Classification ◽  
Complete Intersections

Homeomorphism classification of complex projective complete intersections of dimensions 5, 6 and 7

2009 ◽  
Vol 266 (3) ◽  
pp. 719-746 ◽  
Author(s):  
Fuquan Fang ◽  
Jianbo Wang
Keyword(s):  
Complete Intersections ◽  
Complex Projective

Varieties with nef diagonal

2019 ◽  
Vol 31 (02) ◽  
pp. 2050011 ◽  
Author(s):  
Taku Suzuki ◽  
Kiwamu Watanabe
Keyword(s):  
Projective Variety ◽  
Smooth Projective Variety ◽  
Complete Intersections ◽  
Spherical Varieties ◽  
Del Pezzo

For a smooth projective variety [Formula: see text], we consider when the diagonal [Formula: see text] is nef as a cycle on [Formula: see text]. In particular, we give a classification of complete intersections and smooth del Pezzo varieties where the diagonal is nef. We also study the nefness of the diagonal for spherical varieties.

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