scholarly journals The ideal resolution for generic 3-fat points in P2

2004 ◽  
Vol 187 (1-3) ◽  
pp. 99-128 ◽  
Author(s):  
A. Gimigliano ◽  
M. Idà
Keyword(s):  
Fat Points ◽  
The Ideal

scholarly journals Homaloidal nets and ideals of fat points I

2016 ◽  
Vol 19 (1) ◽  
pp. 54-77 ◽  
Author(s):  
Zaqueu Ramos ◽  
Aron Simis
Keyword(s):  
Linear System ◽  
Fat Points ◽  
Base Points ◽  
Algebraic Properties ◽  
The Ideal

We consider plane Cremona maps with proper base points and the base ideal generated by the linear system of forms defining the map. The object of this work is to study the link between the algebraic properties of the base ideal and those of the ideal of these points fattened by the virtual multiplicities arising from the linear system. We reveal conditions which naturally regulate this association, with particular emphasis on the homological side. While most classical numerical inequalities concern the three highest virtual multiplicities, here we emphasize also the role of one single highest multiplicity. In this vein we describe classes of Cremona maps for large and small values of the highest virtual multiplicity. We also deal with the delicate question as to when is the base ideal non-saturated and consider the structure of its saturation.

scholarly journals Some Families of Componentwise Linear Monomial Ideals

2007 ◽  
Vol 187 ◽  
pp. 115-156 ◽  
Author(s):  
Christopher A. Francisco ◽  
Adam Van Tuyl
Keyword(s):  
Polynomial Ring ◽  
Betti Numbers ◽  
Monomial Ideals ◽  
Fat Points ◽  
Graded Betti Numbers ◽  
Alexander Duality ◽  
Componentwise Linear Ideals ◽  
Positive Integers ◽  
The Ideal

AbstractLet R = k[x1,…,xn] be a polynomial ring over a field k. Let J = {j1,…,jt} be a subset of {1,…, n}, and let mJ ⊂ R denote the ideal (xj1,…,xjt). Given subsets J1,…,Js of {1,…, n} and positive integers a1,…,as, we study ideals of the form These ideals arise naturally, for example, in the study of fat points, tetrahedral curves, and Alexander duality of squarefree monomial ideals. Our main focus is determining when ideals of this form are componentwise linear. Using polymatroidality, we prove that I is always componentwise linear when s ≤ 3 or when Ji ∪ Jj = [n] for all i ≠ j. When s ≥ 4, we give examples to show that I may or may not be componentwise linear. We apply these results to ideals of small sets of general fat points in multiprojective space, and we extend work of Fatabbi, Lorenzini, Valla, and the first author by computing the graded Betti numbers in the s = 2 case. Since componentwise linear ideals satisfy the Multiplicity Conjecture of Herzog, Huneke, and Srinivasan when char(k) = 0, our work also yields new cases in which this conjecture holds.

scholarly journals Homaloidal nets and ideals of fat points II: Subhomaloidal nets

2017 ◽  
Vol 27 (06) ◽  
pp. 677-715 ◽  
Author(s):  
Zaqueu Ramos ◽  
Aron Simis
Keyword(s):  
Linear System ◽  
Linear Systems ◽  
Good Deal ◽  
Detailed Examination ◽  
Symbolic Power ◽  
Fat Points ◽  
Higher Dimensional ◽  
General Plane ◽  
Classical Arithmetic ◽  
The Ideal

This work is a natural sequel to a previous paper by the authors in that it tackles problems of the same nature. Here, one aims at the ideal theoretic and homological properties of an ideal of general plane fat points for which the corresponding second symbolic power has virtual multiplicities of a proper homaloidal type. For this purpose, one carries a detailed examination of the underlying linear system at the initial degree, where a good deal of the results depends on the method of the classical arithmetic quadratic transformations of Hudson–Nagata. A subsidiary guide to understand these ideals through their initial linear systems has been supplied by questions of birationality with source [Formula: see text] and target higher dimensional spaces. This leads, in particular, to the retrieval of birational maps studied by Geramita–Gimigliano–Pitteloud, including a few of the celebrated Bordiga–White parameterizations.

Localization of Intracellular Antigens in thin Sections with Ferritin Labeled Antibody

1970 ◽  
Vol 28 ◽  
pp. 174-175
Author(s):  
M.S. Shahrabadi ◽  
T. Yamamoto
Keyword(s):  
Bovine Serum Albumin ◽  
Bovine Serum ◽  
Antigenic Determinants ◽  
Conjugate Prior ◽  
Thin Sections ◽  
Specific Attachment ◽  
Intracellular Antigen ◽  
Antigen Antibody ◽  
Ideal Method ◽  
The Ideal

The technique of labeling of macromolecules with ferritin conjugated antibody has been successfully used for extracellular antigen by means of staining the specimen with conjugate prior to fixation and embedding. However, the ideal method to determine the location of intracellular antigen would be to do the antigen-antibody reaction in thin sections. This technique contains inherent problems such as the destruction of antigenic determinants during fixation or embedding and the non-specific attachment of conjugate to the embedding media. Certain embedding media such as polyampholytes (2) or cross-linked bovine serum albumin (3) have been introduced to overcome some of these problems.

Criteria and Methods for Reliable Three-Dimensional Image Reconstruction

1974 ◽  
Vol 32 ◽  
pp. 330-331
Author(s):  
R. A. Crowther
Keyword(s):  
Image Reconstruction ◽  
Finite Number ◽  
Density Distribution ◽  
Electron Micrographs ◽  
Mathematical Problem ◽  
Three Dimensional ◽  
Ideal Case ◽  
Dimensional Image ◽  
General Object ◽  
The Ideal

The reconstruction of a three-dimensional image of a specimen from a set of electron micrographs reduces, under certain assumptions about the imaging process in the microscope, to the mathematical problem of reconstructing a density distribution from a set of its plane projections.In the absence of noise we can formulate a purely geometrical criterion, which, for a general object, fixes the resolution attainable from a given finite number of views in terms of the size of the object. For simplicity we take the ideal case of projections collected by a series of m equally spaced tilts about a single axis.

X-Ray Analysis of Frozen Hydrated Sections:The Unconventional Approach

1982 ◽  
Vol 40 ◽  
pp. 754-757
Author(s):  
R. Beeuwkes ◽  
A. Saubermann ◽  
P. Echlin ◽  
S. Churchill
Keyword(s):  
Ratio Method ◽  
Frozen Sections ◽  
Technical Problems ◽  
Sample Handling ◽  
X Ray ◽  
Common Group ◽  
Ideal Method ◽  
Classic Paper ◽  
Physical Principles ◽  
The Ideal

Fifteen years ago, Hall described clearly the advantages of the thin section approach to biological x-ray microanalysis, and described clearly the ratio method for quantitive analysis in such preparations. In this now classic paper, he also made it clear that the ideal method of sample preparation would involve only freezing and sectioning at low temperature. Subsequently, Hall and his coworkers, as well as others, have applied themselves to the task of direct x-ray microanalysis of frozen sections. To achieve this goal, different methodological approachs have been developed as different groups sought solutions to a common group of technical problems. This report describes some of these problems and indicates the specific approaches and procedures developed by our group in order to overcome them. We acknowledge that the techniques evolved by our group are quite different from earlier approaches to cryomicrotomy and sample handling, hence the title of our paper. However, such departures from tradition have been based upon our attempt to apply basic physical principles to the processes involved. We feel we have demonstrated that such a break with tradition has valuable consequences.

High Resolution Study of Polytypism: Application to SiC and Au3 Mn

1982 ◽  
Vol 40 ◽  
pp. 540-541
Author(s):  
G. Van Tendeloo ◽  
J. Van Landuyt ◽  
S. Amelinckx
Keyword(s):  
Electron Microscopy ◽  
High Resolution ◽  
Stacking Sequence ◽  
X Ray ◽  
Powerful Technique ◽  
Resolution Study ◽  
The Ideal

Polytypism has been studied for a number of years and a wide variety of stacking sequences has been detected and analysed. SiC is the prototype material in this respect; see e.g. Electron microscopy under high resolution conditions when combined with x-ray measurements is a very powerful technique to elucidate the correct stacking sequence or to study polytype transformations and deviations from the ideal stacking sequence.

Possible applications of fraunhofer holography in high resolution electron microscopy

1978 ◽  
Vol 36 (1) ◽  
pp. 222-223 ◽  
Author(s):  
N. Bonnet ◽  
M. Troyon ◽  
P. Gallion
Keyword(s):  
Electron Microscopy ◽  
High Resolution ◽  
Transfer Function ◽  
Radiation Damage ◽  
High Resolution Electron Microscopy ◽  
Far Field ◽  
Field Region ◽  
Crystalline Materials ◽  
Resolution Electron ◽  
The Ideal

Two main problems in high resolution electron microscopy are first, the existence of gaps in the transfer function, and then the difficulty to find complex amplitude of the diffracted wawe from registered intensity. The solution of this second problem is in most cases only intended by the realization of several micrographs in different conditions (defocusing distance, illuminating angle, complementary objective apertures…) which can lead to severe problems of contamination or radiation damage for certain specimens.Fraunhofer holography can in principle solve both problems stated above (1,2). The microscope objective is strongly defocused (far-field region) so that the two diffracted beams do not interfere. The ideal transfer function after reconstruction is then unity and the twin image do not overlap on the reconstructed one.We show some applications of the method and results of preliminary tests.Possible application to the study of cavitiesSmall voids (or gas-filled bubbles) created by irradiation in crystalline materials can be observed near the Scherzer focus, but it is then difficult to extract other informations than the approximated size.

The DQE of an electron image recording system

1978 ◽  
Vol 36 (1) ◽  
pp. 100-101
Author(s):  
K.-H. Herrmann ◽  
D. Krahl ◽  
H.-P Rust
Keyword(s):  
Primary Electron ◽  
Ideal Case ◽  
Image Recording ◽  
Main Requirement ◽  
High Detection ◽  
Electron Image ◽  
Video Amplifier ◽  
Detection Quantum Efficiency ◽  
Selection Of ◽  
The Ideal

The high detection quantum efficiency (DQE) is the main requirement for an imagerecording system used in electron microscopy of radiation-sensitive specimens. An electronic TV system of the type shown in Fig. 1 fulfills these conditions and can be used for either analog or digital image storage and processing [1], Several sources of noise may reduce the DQE, and therefore a careful selection of various elements is imperative.The noise of target and of video amplifier can be neglected when the converter stages produce sufficient target electrons per incident primary electron. The required gain depends on the type of the tube and also on the type of the signal processing chosen. For EBS tubes, for example, it exceeds 10. The ideal case, in which all impinging electrons create uniform charge peaks at the target, is not obtainable for several reasons, and these will be discussed as they relate to a system with a scintillator, fiber-optic and photo-cathode combination as the first stage.

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