scholarly journals The perfect cone compactification of quotients of type IV domains

2021 ◽  
Author(s):  
Luca Giovenzana
Keyword(s):  
Moduli Space ◽  
Type Iv ◽  
Symmetric Varieties ◽  
Branch Divisor

AbstractThe perfect cone compactification is a toroidal compactification which can be defined for locally symmetric varieties. Let $$\overline{D_{L}/\widetilde{O}^{+}(L)}^{p}$$ D L / O ~ + ( L ) ¯ p be the perfect cone compactification of the quotient of the type IV domain $$D_{L}$$ D L associated to an even lattice L. In our main theorem we show that the pair $${ (\overline{D_{L}/\widetilde{O}^{+}(L)}^{p}, \Delta /2) }$$ ( D L / O ~ + ( L ) ¯ p , Δ / 2 ) has klt singularities, where $$\Delta $$ Δ is the closure of the branch divisor of $${ D_{L}/\widetilde{O}^{+}(L) }$$ D L / O ~ + ( L ) . In particular this applies to the perfect cone compactification of the moduli space of 2d-polarised K3 surfaces with ADE singularities when d is square-free.

Birational geometry of the moduli space of quartic  surfaces

2019 ◽  
Vol 155 (9) ◽  
pp. 1655-1710
Author(s):  
Radu Laza ◽  
Kieran O’Grady
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
Invariant Theory ◽  
Geometric Invariant Theory ◽  
Dimensional Case ◽  
Geometric Invariant ◽  
Type Iv ◽  
Log Canonical ◽  
Symmetric Varieties ◽  
The Relationship

By work of Looijenga and others, one understands the relationship between Geometric Invariant Theory (GIT) and Baily–Borel compactifications for the moduli spaces of degree-$2$ $K3$ surfaces, cubic fourfolds, and a few other related examples. The similar-looking cases of degree-$4$ $K3$ surfaces and double Eisenbud–Popescu–Walter (EPW) sextics turn out to be much more complicated for arithmetic reasons. In this paper, we refine work of Looijenga in order to handle these cases. Specifically, in analogy with the so-called Hassett–Keel program for the moduli space of curves, we study the variation of log canonical models for locally symmetric varieties of Type IV associated to $D$-lattices. In particular, for the $19$-dimensional case, we conjecturally obtain a continuous one-parameter interpolation between the GIT and Baily–Borel compactifications for the moduli of degree-$4$ $K3$ surfaces. The analogous $18$-dimensional case, which corresponds to hyperelliptic degree-$4$ $K3$ surfaces, can be verified by means of Variation of Geometric Invariant Theory (VGIT) quotients.

scholarly journals Moduli spaces of irreducible symplectic manifolds

2010 ◽  
Vol 146 (2) ◽  
pp. 404-434 ◽  
Author(s):  
V. Gritsenko ◽  
K. Hulek ◽  
G. K. Sankaran
Keyword(s):  
Moduli Space ◽  
Moduli Spaces ◽  
General Type ◽  
Symplectic Manifolds ◽  
Symmetric Varieties

AbstractWe study the moduli spaces of polarised irreducible symplectic manifolds. By a comparison with locally symmetric varieties of orthogonal type of dimension 20, we show that the moduli space of polarised deformation K3[2]manifolds with polarisation of degree 2dand split type is of general type ifd≥12.

The LDE-Type Flare Occurrence (1969-1993)

1994 ◽  
Vol 144 ◽  
pp. 279-282
Author(s):  
A. Antalová
Keyword(s):  
Time Series ◽  
Fourier Analysis ◽  
Sunspot Cycle ◽  
List Type ◽  
Type Number ◽  
Solar Cycles ◽  
Type Iv ◽  
Long Duration ◽  
Cycle Maximum ◽  
Flare Index

AbstractThe occurrence of LDE-type flares in the last three cycles has been investigated. The Fourier analysis spectrum was calculated for the time series of the LDE-type flare occurrence during the 20-th, the 21-st and the rising part of the 22-nd cycle. LDE-type flares (Long Duration Events in SXR) are associated with the interplanetary protons (SEP and STIP as well), energized coronal archs and radio type IV emission. Generally, in all the cycles considered, LDE-type flares mainly originated during a 6-year interval of the respective cycle (2 years before and 4 years after the sunspot cycle maximum). The following significant periodicities were found:• in the 20-th cycle: 1.4, 2.1, 2.9, 4.0, 10.7 and 54.2 of month,• in the 21-st cycle: 1.2, 1.6, 2.8, 4.9, 7.8 and 44.5 of month,• in the 22-nd cycle, till March 1992: 1.4, 1.8, 2.4, 7.2, 8.7, 11.8 and 29.1 of month,• in all interval (1969-1992):a)the longer periodicities: 232.1, 121.1 (the dominant at 10.1 of year), 80.7, 61.9 and 25.6 of month,b)the shorter periodicities: 4.7, 5.0, 6.8, 7.9, 9.1, 15.8 and 20.4 of month.Fourier analysis of the LDE-type flare index (FI) yields significant peaks at 2.3 - 2.9 months and 4.2 - 4.9 months. These short periodicities correspond remarkably in the all three last solar cycles. The larger periodicities are different in respective cycles.

Labelling of non-A, non-B hepatitis infected chimpanzee hepatocytes with nuclease-gold conjugates

1984 ◽  
Vol 42 ◽  
pp. 250-251
Author(s):  
G. D. Gagne ◽  
M. F. Miller ◽  
D. A. Peterson
Keyword(s):  
Endoplasmic Reticulum ◽  
Experimental Infection ◽  
Uranyl Acetate ◽  
Type I ◽  
Cellular Injury ◽  
Type Ii ◽  
Tubular Structures ◽  
Type Iii ◽  
Type Iv ◽  
Infected Chimpanzee

Experimental infection of chimpanzees with non-A, non-B hepatitis (NANB) or with delta agent hepatitis results in the appearance of characteristic cytoplasmic alterations in the hepatocytes. These alterations include spongelike inclusions (Type I), attached convoluted membranes (Type II), tubular structures (Type III), and microtubular aggregates (Type IV) (Fig. 1). Type I, II and III structures are, by association, believed to be derived from endoplasmic reticulum and may be morphogenetically related. Type IV structures are generally observed free in the cytoplasm but sometimes in the vicinity of type III structures. It is not known whether these structures are somehow involved in the replication and/or assembly of the putative NANB virus or whether they are simply nonspecific responses to cellular injury. When treated with uranyl acetate, type I, II and III structures stain intensely as if they might contain nucleic acids. If these structures do correspond to intermediates in the replication of a virus, one might expect them to contain DNA or RNA and the present study was undertaken to explore this possibility.

Effects of EDTA, Hyaluronidase and Collagenase on Epiphyseal Cartilage Matrix

1968 ◽  
Vol 26 ◽  
pp. 56-57
Author(s):  
H. Clarke Anderson ◽  
Priscilla R. Coulter
Keyword(s):  
Light And Electron Microscopy ◽  
Matrix Vesicles ◽  
Cartilage Matrix ◽  
Collagen Fibrils ◽  
Epiphyseal Cartilage ◽  
Dense Matrix ◽  
Type Iv ◽  
Bovine Testicular Hyaluronidase ◽  
The Matrix ◽  
Testicular Hyaluronidase

Epiphyseal cartilage matrix contains fibrils and particles of at least 5 different types: 1. Banded collagen fibrils, present throughout the matrix, but not seen in the lacunae. 2. Non-periodic fine fibrils <100Å in diameter (Fig. 1), which are most notable in the lacunae, and may represent immature collagen. 3. Electron dense matrix granules (Fig. 1) which are often attached to fine fibrils and collagen fibrils, and probably contain protein-polysaccharide although the possibility of a mineral content has not been excluded. 4. Matrix vesicles (Fig. 2) which show a selective distribution throughout the epiphysis, and may play a role in calcification. 5. Needle-like apatite crystals (Fig. 2).Blocks of formalin-fixed epiphysis from weanling mice were digested with the following agents in 0.1M phosphate buffer: a) 5% ethylenediaminetetraacetate (EDTA) at pH 8.3, b) 0.015% bovine testicular hyaluronidase (Sigma, type IV, 750 units/mg) at pH 5.5, and c) 0.1% collagenase (Worthington, chromatograhically pure, 200 units/mg) at pH 7.4. All digestions were carried out at 37°C overnight. Following digestion tissues were examined by light and electron microscopy to determine changes in the various fibrils and particles of the matrix.

Fine Structure of Type IV Glycogenosis

1981 ◽  
Vol 39 ◽  
pp. 464-465
Author(s):  
P.K. Simons
Keyword(s):  
Needle Biopsy ◽  
Tissue Concentration ◽  
Inborn Errors ◽  
Rare Type ◽  
Type Iv ◽  
Iron Copper ◽  
Proper Diagnosis ◽  
Type Iv Glycogenosis ◽  
Loss Of Appetite ◽  
Enzymatic Defect

Glycogenosis is defined as any condition in which the tissue concentration of glycogen is increased. There are currently ten recognized variants of glycogenosis that are heritable inborn errors of metabolism. The specific enzymatic defect in each of the variants is known or at least suspected. In all cases, the enzymatic defect prevents the proper metabolism or formation of the glycogen molecule. The clinical and histologic differences between the types of glycogenosis is important to a proper diagnosis after the presence of such a condition is realized. This study was initiated to examine the ultrastructure of the rare Type IV Glycogenosis (Amylopectinosis) of which there is very little morphologic characterization in the literature.Liver tissue was obtained by needle biopsy from a 12-month-old Oriental female who was originally admitted to the hospital after observation of poor development, loss of appetite, and hepatomegaly. The majority of the tissue was fixed for light microscopy in neutral buffered formalin and processed using routine and special staining procedures (reticulin, trichrome, iron, copper, PAS, PAS-diastase and PAS-pectinase.

Biodegradable polyester neuroprostheses promote the reconnection of separated peripheral nerve stubs

1992 ◽  
Vol 50 (2) ◽  
pp. 1094-1095
Author(s):  
Beverly L. Giammara ◽  
Jennifer S. Stevenson ◽  
Peggy E. Yates ◽  
Robert H. Gunderson ◽  
Jacob S. Hanker
Keyword(s):  
Image Analysis ◽  
Basement Membrane ◽  
Periodic Acid ◽  
Light And Electron Microscopy ◽  
Computer Assisted ◽  
Type Iii Collagen ◽  
Image Analysis System ◽  
Biodegradable Polyester ◽  
Adult Rats ◽  
Type Iv

An 11mm length of sciatic nerve was removed from 10 anesthetized adult rats and replaced by a biodegradable polyester Vicryl™ mesh sleeve which was then injected with the basement membrane gel, Matrigel™. It was noted that leg sensation and movement were much improved after 30 to 45 days and upon sacrifice nerve reconnection was noted in all animals. Epoxy sections of the repaired nerves were compared with those of the excised segments by the use of a variation of the PAS reaction, the PATS reaction, developed in our laboratories for light and electron microscopy. This microwave-accelerated technique employs periodic acid, thiocarbohydrazide and silver methenamine. It stains basement membrane or Type IV collagen brown and type III collagen (reticulin), axons, Schwann cells, endoneurium and perineurium black. Epoxy sections of repaired and excised nerves were also compared by toluidine blue (tb) staining. Comparison of the sections of control and repaired nerves was done by computer-assisted microscopic image analysis using an Olympus CUE-2 Image Analysis System.

The distribution and density of ciliary tufts on the siphons of Anodonta cygnea (Mollusca: Bivalvia)

1990 ◽  
Vol 48 (3) ◽  
pp. 518-519
Author(s):  
Wen-lung Wu
Keyword(s):  
Osmium Tetroxide ◽  
Internal Surface ◽  
Mechanical Stimuli ◽  
Type Ii ◽  
Sensory Receptors ◽  
Anodonta Cygnea ◽  
Type Iv ◽  
Sem Study ◽  
Inhalant Siphon ◽  
Type V

The mantle of bivalves has come entirely to enclose the laterally compressed body and the mantle margin has assumed a variety of functions, one of the pricipal ones being sensory. Ciliary tufts, which are probably sensory, have been reported from the mantle and siphons of several bivalves1∽4. Certain regions of the mantle margin are likely to be more or less, sensitive to certain stimuli than others. The inhalant siphon is likely to be particularly sensitive to both chemical and mechanical stimuli, whereas the exhalant siphon will be less sensitive to both. The distribution and density of putative sensory receptors on the in-and ex-halant siphon is compared in this paper.The excised siphons were fixed in glutaraldehyde and osmium tetroxide, the whole procedure of SEM study is recorded in Wu's thesis.Type II cilia cover the tips of tentacles, 6.13um. Type IV and type V cilia are found on the surface of tentacles. Type IV cilia are occasionally present at the tips of tentacles, 8 um long. They are the commonest type on the surface of tentacles. Type VI cilia occor in the internal surface of the inhalant siphon, but are not found on the surface of tentacles, 6.7-10um long.

The use of 1nm silver enhanced gold probes for the detection of skin antigens

1990 ◽  
Vol 48 (3) ◽  
pp. 902-903
Author(s):  
J.P Cassella ◽  
H. Shimizu ◽  
A. Ishida-Yamamoto ◽  
R.A.J. Eady
Keyword(s):  
Type Iv Collagen ◽  
Freeze Substitution ◽  
Collagen Type Iv ◽  
Electron Microscopic ◽  
Normal Human Skin ◽  
Type Iv ◽  
Type Vii Collagen ◽  
Keratin Filaments ◽  
Normal Human ◽  
Phosphate Buffered Saline

1nm colloidal gold with silver enhancement has been used in conjunction with a low-temperature post-embedding (post-E) technique for the demonstration of skin antigens at both the light microscopic (LM) and electron microscopic (EM) levels.Keratin filaments and basement membrane zone (BMZ) associated antigens in normal human skin (NHS) were immunolabelled using antibodies against keratin 14, 10, and 1, the carboxy-terminus and collagenous portion of type VII collagen, type IV collagen and bullous pemphigoid antigen (BP-Ag).Fresh samples of NHS were cryoprotected in 15% glycerol, cryofixed in propane at -190°C, subjected to freeze substitution in methanol at -80°C and embedded in Lowicryl K11M at -60°C. Polymerisation of the resin was initiated under UVR at - 60°C for 48 hours and continued at room temperature for a further 48 hours. Semith in sections were air dried onto slides coated with 3-aminopropyltriethoxysilane. The following immunolabelling protocol was adopted: Primary antibody was applied for 2 hours at 37°C or overnight at 4°C. Following washing in Dulbecco’s phosphate buffered saline (PBSA) a biotinylated secondary antibody was applied for 2 hours at 37°C. The sections were further washed in PBSA and 1nm gold avidin was applied. Sections were finally washed in PBSA and silver enhanced.

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