scholarly journals Completing the Classification of Representations of SLn with Complete Intersection Invariant Ring

2020 ◽  
Author(s):  
LUKAS BRAUN
Keyword(s):  
Complete Intersection ◽  
Invariant Ring

Castelnuovo-Mumford regularity bound for smooth threefolds in ℙ5 and extremal examples

1999 ◽  
Vol 1999 (509) ◽  
pp. 21-34
Author(s):  
Si-Jong Kwak
Keyword(s):  
Complete Intersection ◽  
Number Field ◽  
Complex Number ◽  
Smooth Surfaces ◽  
Veronese Surface ◽  
Optimal Bound ◽  
Integral Curves ◽  
Complex Number Field

Abstract Let X be a nondegenerate integral subscheme of dimension n and degree d in ℙN defined over the complex number field ℂ. X is said to be k-regular if Hi(ℙN, ℐX (k – i)) = 0 for all i ≧ 1, where ℐX is the sheaf of ideals of ℐℙN and Castelnuovo-Mumford regularity reg(X) of X is defined as the least such k. There is a well-known conjecture concerning k-regularity: reg(X) ≦ deg(X) – codim(X) + 1. This regularity conjecture including the classification of borderline examples was verified for integral curves (Castelnuovo, Gruson, Lazarsfeld and Peskine), and an optimal bound was also obtained for smooth surfaces (Pinkham, Lazarsfeld). It will be shown here that reg(X) ≦ deg(X) – 1 for smooth threefolds X in ℙ5 and that the only extremal cases are the rational cubic scroll and the complete intersection of two quadrics. Furthermore, every smooth threefold X in ℙ5 is k-normal for all k ≧ deg(X) – 4, which is the optimal bound as the Palatini 3-fold of degree 7 shows. The same bound also holds for smooth regular surfaces in ℙ4 other than for the Veronese surface.

AN ATTEMPT AT A NEW CLASSIFICATION OF CICY MANIFOLDS

1994 ◽  
Vol 09 (38) ◽  
pp. 3585-3593 ◽  
Author(s):  
M. GAGNON ◽  
Q. HO-KIM
Keyword(s):  
Complete Intersection ◽  
New Classification ◽  
Calabi Yau Manifolds

Using a recently proposed list of 97,360 complete intersection Calabi-Yau manifolds, we attempt to select some promising three- and four-generation manifolds. We classify the configurations surviving the selection tests by breaking the associated diagrams into kernels and extensions and by regrouping configurations having the same kernels into families. The resulting classification for the surviving three- and four-generation manifolds is presented.

scholarly journals Subcategories of singularity categories via tensor actions

2013 ◽  
Vol 150 (2) ◽  
pp. 229-272 ◽  
Author(s):  
Greg Stevenson
Keyword(s):  
Complete Intersection ◽  
Analogous Result ◽  
Complete Classification ◽  
Derived Category ◽  
Hypersurface Singularities ◽  
Regular Scheme ◽  
Affine Scheme

AbstractWe obtain, via the formalism of tensor actions, a complete classification of the localizing subcategories of the stable derived category of any affine scheme that has hypersurface singularities or is a complete intersection in a regular scheme; in particular, this classifies the thick subcategories of the singularity categories of such rings. The analogous result is also proved for certain locally complete intersection schemes. It is also shown that from each of these classifications one can deduce the (relative) telescope conjecture.

A classifier for simple isolated complete intersection singularities

2015 ◽  
Vol 52 (1) ◽  
pp. 1-11
Author(s):  
Deeba Afzal ◽  
Gerhard Pfister
Keyword(s):  
Complete Intersection ◽  
Computer Algebra ◽  
Computer Algebra System

M. Giusti’s classification of the simple complete intersection singularities is characterized in terms of invariants. This is a basis for the implementation of a classifier in the computer algebra system Singular.

Note on the spectral classification of carbon stars in the photographic infrared region

1966 ◽  
Vol 24 ◽  
pp. 21-23
Author(s):  
Y. Fujita
Keyword(s):  
Infrared Region ◽  
Spectral Classification ◽  
Carbon Stars

We have investigated the spectrograms (dispersion: 8Å/mm) in the photographic infrared region fromλ7500 toλ9000 of some carbon stars obtained by the coudé spectrograph of the 74-inch reflector attached to the Okayama Astrophysical Observatory. The names of the stars investigated are listed in Table 1.

Diagnostic Value of Electron Microscopy in Soft Tissue Tumors

1970 ◽  
Vol 28 ◽  
pp. 220-221
Author(s):  
Gerald Fine ◽  
Azorides R. Morales
Keyword(s):  
Cardiac Myxoma ◽  
Osteogenic Sarcoma ◽  
Diagnostic Value ◽  
Soft Tissue Tumors ◽  
Amelanotic Melanoma ◽  
Growth Patterns ◽  
Light Microscopic Level ◽  
Mesenchymal Tumors ◽  
Good Agreement

For years the separation of carcinoma and sarcoma and the subclassification of sarcomas has been based on the appearance of the tumor cells and their microscopic growth pattern and information derived from certain histochemical and special stains. Although this method of study has produced good agreement among pathologists in the separation of carcinoma from sarcoma, it has given less uniform results in the subclassification of sarcomas. There remain examples of neoplasms of different histogenesis, the classification of which is questionable because of similar cytologic and growth patterns at the light microscopic level; i.e. amelanotic melanoma versus carcinoma and occasionally sarcoma, sarcomas with an epithelial pattern of growth simulating carcinoma, histologically similar mesenchymal tumors of different histogenesis (histiocytoma versus rhabdomyosarcoma, lytic osteogenic sarcoma versus rhabdomyosarcoma), and myxomatous mesenchymal tumors of diverse histogenesis (myxoid rhabdo and liposarcomas, cardiac myxoma, myxoid neurofibroma, etc.)

Ultrastructure of mesotheliomas

1984 ◽  
Vol 42 ◽  
pp. 98-101
Author(s):  
Irving Dardick
Keyword(s):  
Electron Microscopy ◽  
Latent Period ◽  
Spindle Cell ◽  
Spindle Cell Sarcoma ◽  
Metastatic Adenocarcinoma ◽  
Cell Sarcoma ◽  
Cytological Features ◽  
Industrial Use ◽  
Degree Of Differentiation

With the extensive industrial use of asbestos in this century and the long latent period (20-50 years) between exposure and tumor presentation, the incidence of malignant mesothelioma is now increasing. Thus, surgical pathologists are more frequently faced with the dilemma of differentiating mesothelioma from metastatic adenocarcinoma and spindle-cell sarcoma involving serosal surfaces. Electron microscopy is amodality useful in clarifying this problem.In utilizing ultrastructural features in the diagnosis of mesothelioma, it is essential to appreciate that the classification of this tumor reflects a variety of morphologic forms of differing biologic behavior (Table 1). Furthermore, with the variable histology and degree of differentiation in mesotheliomas it might be expected that the ultrastructure of such tumors also reflects a range of cytological features. Such is the case.

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