scholarly journals On crepant resolutions of 2-parameter series of Gorenstein cyclic quotient singularities

1998 ◽  
Vol 33 (3-4) ◽  
pp. 208-265 ◽  
Author(s):  
Dimitrios I. Dais ◽  
Utz-Uwe Haus ◽  
Martin Henk
Keyword(s):  
Quotient Singularities ◽  
Crepant Resolutions ◽  
Cyclic 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

scholarly journals VANISHING OF THE NEGATIVE HOMOTOPY -THEORY OF QUOTIENT SINGULARITIES

2017 ◽  
Vol 18 (3) ◽  
pp. 619-627
Author(s):  
Gonçalo Tabuada
Keyword(s):  
Algebraic Geometry ◽  
Upper Bound ◽  
Homotopy Theory ◽  
Krull Dimension ◽  
Noncommutative Algebraic Geometry ◽  
Noetherian Scheme ◽  
Quotient Singularities ◽  
Cyclic Quotient Singularities

Making use of Gruson–Raynaud’s technique of ‘platification par éclatement’, Kerz and Strunk proved that the negative homotopy$K$-theory groups of a Noetherian scheme$X$of Krull dimension$d$vanish below$-d$. In this article, making use of noncommutative algebraic geometry, we improve this result in the case of quotient singularities by proving that the negative homotopy$K$-theory groups vanish below$-1$. Furthermore, in the case of cyclic quotient singularities, we provide an explicit ‘upper bound’ for the first negative homotopy$K$-theory group.

scholarly journals On hypersurface quotient singularities of dimension 4

2004 ◽  
Vol 2004 (48) ◽  
pp. 2547-2581
Author(s):  
Li Chiang ◽  
Shi-Shyr Roan
Keyword(s):  
Abelian Group ◽  
Hilbert Scheme ◽  
Alternating Group ◽  
Detailed Structure ◽  
Special Group ◽  
Standard Representation ◽  
Quotient Singularities ◽  
Crepant Resolutions

We consider geometrical problems on Gorenstein hypersurface orbifolds of dimensionn≥4through the theory of Hilbert scheme of group orbits. For a linear special groupGacting onℂn, we study theG-Hilbert schemeHilbG(ℂn)and crepant resolutions ofℂn/GforGtheA-type abelian groupAr(n). Forn=4, we obtain the explicit structure ofHilbAr(4)(ℂ4). The crepant resolutions ofℂ4/Ar(4)are constructed through their relation withHilbAr(4)(ℂ4), and the connections between these crepant resolutions are found by the “flop” procedure of 4-folds. We also make some primitive discussion onHilbG(ℂn)forGthe alternating group𝔄n+1of degreen+1with the standard representation onℂn; the detailed structure ofHilb𝔄4(ℂ3)is explicitly constructed.

scholarly journals Crepant Resolutions of 3-Dimensional Quotient Singularities via Cox Rings

2017 ◽  
Vol 28 (2) ◽  
pp. 161-180
Author(s):  
Maria Donten-Bury ◽  
Maksymilian Grab
Keyword(s):  
3 Dimensional ◽  
Cox Rings ◽  
Quotient Singularities ◽  
Crepant Resolutions

scholarly journals On the Milnor fibres of cyclic quotient singularities

2010 ◽  
Vol 101 (2) ◽  
pp. 554-588 ◽  
Author(s):  
András Némethi ◽  
Patrick Popescu-Pampu
Keyword(s):  
Quotient Singularities ◽  
Cyclic Quotient Singularities

Stable quintuples and terminal quotient singularities

1990 ◽  
Vol 107 (1) ◽  
pp. 91-101 ◽  
Author(s):  
G. K. Sankaran
Keyword(s):  
Algebraic Geometry ◽  
Geometry Of Numbers ◽  
Quotient Singularities ◽  
Cyclic Quotient Singularities

We shall prove below part of a conjecture made by Shigefumi Mori, David Morrison and Ian Morrison in the course of their investigations into the properties of isolated terminal cyclic quotient singularities of prime Gorenstein index in dimension four [1]. The reader of the present paper need have no knowledge of algebraic geometry, because we quickly reduce the problem to one about the geometry of numbers that can be solved by elementary calculations. The calculations are very lengthy and not quite routine, so what the reader does need is either patience, if he intends to check them, or faith, if he does not. We give only part of the calculations below. Full details may be obtained from the author.*

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