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 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 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 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.

ON c1 = 0 RESOLUTION OF QUOTIENT SINGULARITY

1994 ◽  
Vol 05 (04) ◽  
pp. 523-536 ◽  
Author(s):  
SHI-SHYR ROAN
Keyword(s):  
Euler Characteristic ◽  
Group Action ◽  
Euler Number ◽  
Quotient Singularity ◽  
3 Dimensional ◽  
Icosahedral Group ◽  
Higher Dimensional ◽  
Quotient Singularities

An explicit c1 = 0 resolution of the 3-dimensional quotient singularity by the icosahedral group is constructed. Moreover, the Euler number of this resolution is identified with the orbifold Euler characteristic of the group action. Examples of c1 = 0 resolutions of higher dimensional quotient singularities are also obtained.

Three-Dimensional Reconstruction Using Stereo Pairs from Serial Thick Sections

1977 ◽  
Vol 35 ◽  
pp. 562-563
Author(s):  
Robert Glaeser ◽  
Thomas Bauer ◽  
David Grano
Keyword(s):  
Three Dimensional ◽  
Dimensional Structure ◽  
Serial Sections ◽  
Thin Sections ◽  
3 Dimensional ◽  
Transmission Electron ◽  
Freeze Dried ◽  
Dimensional Reconstruction ◽  
Stereo Imagery ◽  
Whole Mounts

In transmission electron microscopy, the 3-dimensional structure of an object is usually obtained in one of two ways. For objects which can be included in one specimen, as for example with elements included in freeze- dried whole mounts and examined with a high voltage microscope, stereo pairs can be obtained which exhibit the 3-D structure of the element. For objects which can not be included in one specimen, the 3-D shape is obtained by reconstruction from serial sections. However, without stereo imagery, only detail which remains constant within the thickness of the section can be used in the reconstruction; consequently, the choice is between a low resolution reconstruction using a few thick sections and a better resolution reconstruction using many thin sections, generally a tedious chore. This paper describes an approach to 3-D reconstruction which uses stereo images of serial thick sections to reconstruct an object including detail which changes within the depth of an individual thick section.

Structural preservation and absolute contrast of catalase crystal sections prepared with tannic acid

1983 ◽  
Vol 41 ◽  
pp. 448-449
Author(s):  
C.W. Akey ◽  
M. Szalay ◽  
S.J. Edelstein
Keyword(s):  
Tannic Acid ◽  
Beef Heart ◽  
X Rays ◽  
Screw Axis ◽  
General Applicability ◽  
Thin Sections ◽  
Beef Liver ◽  
3 Dimensional ◽  
Dimensional Reconstruction ◽  
Structural Preservation

Three methods of obtaining 20 Å resolution in sectioned protein crystals have recently been described. They include tannic acid fixation, low temperature embedding and grid sectioning. To be useful for 3-dimensional reconstruction thin sections must possess suitable resolution, structural fidelity and a known contrast. Tannic acid fixation appears to satisfy the above criteria based on studies of crystals of Pseudomonas cytochrome oxidase, orthorhombic beef liver catalase and beef heart F1-ATPase. In order to develop methods with general applicability, we have concentrated our efforts on a trigonal modification of catalase which routinely demonstrated a resolution of 40 Å. The catalase system is particularly useful since a comparison with the structure recently solved with x-rays will permit evaluation of the accuracy of 3-D reconstructions of sectioned crystals.Initially, we re-evaluated the packing of trigonal catalase crystals studied by Longley. Images of the (001) plane are of particular interest since they give a projection down the 31-screw axis in space group P3121. Images obtained by the method of Longley or by tannic acid fixation are negatively contrasted since control experiments with orthorhombic catalase plates yield negatively stained specimens with conditions used for the larger trigonal crystals.

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