scholarly journals A Note on the Differential Forms on Everywhere Normal Varieties

1951 ◽  
Vol 2 ◽  
pp. 93-94
Author(s):  
Yûsaku Kawahara
Keyword(s):  
Algebraic Geometry ◽  
Differential Form ◽  
Differential Forms ◽  
Multiple Point ◽  
Algebraic Varieties ◽  
Simple Point ◽  
Multiple Points ◽  
Complete Variety ◽  
Normal Variety ◽  
Normal Varieties

A. Weil proposed in his book “Foundations of algebraic geometry” several problems concerning differential forms on algebraic varieties, S. Koizumi has proved that if ω is a differential form on a complete variety U without multiple point, which is finite at every point of IT, then ω is the differential form of the first kind. The following example shows that on everywhere normal varieties with multiple points this statement holds no more; that is: A differential form on a everywhere normal variety which is finite on every simple point of its variety is not always the differential form of the first kind.

scholarly journals On the Differential Forms on Algebraic Varieties

1952 ◽  
Vol 4 ◽  
pp. 73-78
Author(s):  
Yûsaku Kawahara
Keyword(s):  
Algebraic Geometry ◽  
Differential Form ◽  
Differential Forms ◽  
Multiple Point ◽  
Algebraic Varieties ◽  
Complete Variety ◽  
Case Characteristic

In the book “Foundations of algebraic geometry” A. Weil proposed the following problem ; does every differential form of the first kind on a complete variety U determine on every subvariety V of U a differential form of the first kind? This problem was solved affirmatively by S. Koizumi when U is a complete variety without multiple point. In this note we answer this problem in affirmative in the case where V is a simple subvariety of a complete variety U (in §1). When the characteristic is 0 we may extend our result to a more general case but this does not hold for the case characteristic p≠0 (in §2).

scholarly journals Remarks on the Differential Forms of the First Kind on Algebraic Varieties

1953 ◽  
Vol 6 ◽  
pp. 37-40
Author(s):  
Yûsaku Kawahara
Keyword(s):  
Differential Form ◽  
Differential Forms ◽  
Algebraic Varieties ◽  
Simple Point ◽  
Generic Point ◽  
Complete Variety ◽  
Field Of Definition ◽  
Common Field

A differential form co on a complete variety Un is said to be of the first kind if it is finite at every simple point of any variety which is birationally equivalent to U. Let k be a common field of definition for Uand ω, and let Pbe a generic point of Uover k. If ω is of the first kind, then ω(P) is of course a differential form of the first kind belonging to the extension k(P) of k.

scholarly journals On the Theory of Differential Forms on Algebraic Varieties

1957 ◽  
Vol 11 ◽  
pp. 13-39
Author(s):  
Yûsaku Kawahara
Keyword(s):  
Function Field ◽  
Projective Variety ◽  
Hyperplane Section ◽  
Differential Forms ◽  
Classical Case ◽  
Algebraic Varieties ◽  
Simple Point ◽  
Perfect Field ◽  
Linearly Independent ◽  
Normal Varieties

Let K be a function field of one variable over a perfect field k and let v be a valuation of K over k. Then is the different-divisor (Verzweigungsdivisor) of K/k(x), and (x)∞ is the denominator-divisor (Nennerdivisor) of x. In §1 we consider a generalization of this theorem in the function fields of many variables under some conditions. In §2 and §3 we consider the differential forms of the first kind on algebraic varieties, or the differential forms which are finite at every simple point of normal varieties and subadjoint hypersurfaces which are developed by Clebsch and Picard in the classical case. In §4 we give a proof of the following theorem. Let Vr be a normal projective variety defined over a field k of characteristic 0, and let ω1, …, ωs be linearly independent simple closed differential forms which are finite at every simple point of Vr. Then the induced forms on a generic hyperplane section are also linearly independent.

scholarly journals On the fundamental groups of normal varieties

2016 ◽  
Vol 18 (04) ◽  
pp. 1550065 ◽  
Author(s):  
Donu Arapura ◽  
Alexandru Dimca ◽  
Richard Hain
Keyword(s):  
Fundamental Groups ◽  
Algebraic Varieties ◽  
Local Systems ◽  
Normal Variety ◽  
Normal Complex ◽  
Normal Varieties ◽  
Rank One

We show that the fundamental groups of normal complex algebraic varieties share many properties of the fundamental groups of smooth varieties. The jump loci of rank one local systems on a normal variety are related to the jump loci of a resolution and of a smoothing of this variety.

scholarly journals Συμβολή εις την μελέτην της αξίας ενιών εμφρακτικών υλικών των ριζικών σωληνών δια ραδιενεργών ισοτόπων (S35)

1967 ◽  
Author(s):  
Ζαχαρίας Μαντζαβίνος
Keyword(s):  
Root Canal ◽  
Multiple Point ◽  
Multiple Points ◽  
Single Root ◽  
Gutta Percha ◽  
Silver Point ◽  
Autoradiographic Technique ◽  
Root Canal Sealers

The present study was performed in order to evaluate, by the autoradiographic technique the sealing properties of three root canal sealers, combined with gutta - percha and silver points, in vitro. A total of one hundred and five extracted human, single root teeth were used and divided into five groups according to the filling combinations tested. The teeth were filled, using two techniques, of the single and multiple points. Autoradiographies, using S35, in all instances, were performed and the results obtained were compared with the respective dental radiograms The obtained results lead to the following conclusions: 1. Silver and gutta - percha points may be always combined with sealers. Otherwise the root canal is not adequately sealed. 2. A gutta - percha point, without sealer, produced a superior filling to silver point. 3. It seems possible to obtain a complete obturation of the rootcanal with the combination of gutta - percha and Grosman’s Sealer using the multiple - point technique. 4. It follows in effectivness, the combination of silver point and Grossman’s sealer.5. The combination of gutta - percha point with Zinc - oxide eugenol sealer and chloropercha are the least efficient. 6. Finally it must be stressed that since the conditions of the present study do not correspond exactly to those encountered in vivo, extrapolation of the results obtained, to man has to be performed with caution.

SKIN TESTING WITH LIQUID OLD TUBERCULIN WITH A MULTIPLE PUNCTURE TECHNIQUE

PEDIATRICS ◽  
1968 ◽  
Vol 42 (3) ◽  
pp. 465-470
Author(s):  
Harvey Kravitz ◽  
Fredric Burg ◽  
Robert B. Lawson
Keyword(s):  
Skin Testing ◽  
Mantoux Test ◽  
Multiple Point ◽  
Plastic Ring ◽  
Multiple Points ◽  
Point Test ◽  
Tuberculin Testing ◽  
High Degree ◽  
Multiple Puncture ◽  
Puncture Technique

An improved multiple puncture technique (MPT) for tuberculin testing is applied with a nine-pointed plastic ring covered by a tube containing a specially concentrated liquid tuberculin. A high degree of positive and negative agreement was obtained with this test when compared to the Mantoux test (PPD, 5 TU). The reactions from the multiple puncture technique are discrete, single, and circular, and they are easy to read and measure. Erythema and induration from this test are smaller than from the Mantoux test (PPD, 5 TU). Children appear to show less fear and felt less pain with the multiple point test than with the Mantoux test. "Wet" tuberculin on multiple points eliminates two possible variables associated with "dry" tuberculin on the points–the length of time that the tines are held in the skin and the moisture content of the skin.

scholarly journals POINCARÉ AND SOBOLEV INEQUALITIES FOR DIFFERENTIAL FORMS IN HEISENBERG GROUPS AND CONTACT MANIFOLDS

2020 ◽  
pp. 1-52
Author(s):  
ANNALISA BALDI ◽  
BRUNO FRANCHI ◽  
PIERRE PANSU
Keyword(s):  
Differential Form ◽  
Scale Invariance ◽  
Differential Forms ◽  
Sobolev Inequalities ◽  
Exact Form ◽  
Heisenberg Groups ◽  
Contact Manifolds ◽  
Bounded Geometry ◽  
Exterior Differential ◽  
Rumin Complex

Abstract In this paper, we prove contact Poincaré and Sobolev inequalities in Heisenberg groups $\mathbb{H}^{n}$ , where the word ‘contact’ is meant to stress that de Rham’s exterior differential is replaced by the exterior differential of the so-called Rumin complex $(E_{0}^{\bullet },d_{c})$ , which recovers the scale invariance under the group dilations associated with the stratification of the Lie algebra of $\mathbb{H}^{n}$ . In addition, we construct smoothing operators for differential forms on sub-Riemannian contact manifolds with bounded geometry, which act trivially on cohomology. For instance, this allows us to replace a closed form, up to adding a controlled exact form, with a much more regular differential form.

scholarly journals On singular sets of flat holomorphic mappings with isolated singularities

1978 ◽  
Vol 70 ◽  
pp. 47-80
Author(s):  
Hideo Omoto
Keyword(s):  
Algebraic Geometry ◽  
Singular Point ◽  
Critical Points ◽  
Euler Number ◽  
Holomorphic Mappings ◽  
Algebraic Varieties ◽  
Isolated Singularities ◽  
General Fiber ◽  
Singular Sets ◽  
Algebraic Maps

In [4] B. Iversen studied critical points of algebraic mappings, using algebraic-geometry methods. In particular when algebraic maps have only isolated singularities, he shows the following relation; Let V and S be compact connected non-singular algebraic varieties of dimcV = n, and dimc S = 1, respectively. Suppose f is an algebraic map of V onto S with isolated singularities. Then it follows thatwhere χ denotes the Euler number, μf(p) is the Milnor number of f at the singular point p, and F is the general fiber of f : V → S.

scholarly journals Extension theorems for differential forms and Bogomolov–Sommese vanishing on log canonical varieties

2009 ◽  
Vol 146 (1) ◽  
pp. 193-219 ◽  
Author(s):  
Daniel Greb ◽  
Stefan Kebekus ◽  
Sándor J. Kovács
Keyword(s):  
Differential Forms ◽  
Natural Generalization ◽  
Resolution Of Singularities ◽  
Vanishing Theorem ◽  
Exceptional Set ◽  
Extension Theorems ◽  
Normal Variety ◽  
Log Canonical ◽  
Smooth Locus

AbstractGiven a normal variety Z, a p-form σ defined on the smooth locus of Z and a resolution of singularities $\pi : \widetilde {Z} \to Z$, we study the problem of extending the pull-back π*(σ) over the π-exceptional set $E \subset \widetilde {Z}$. For log canonical pairs and for certain values of p, we show that an extension always exists, possibly with logarithmic poles along E. As a corollary, it is shown that sheaves of reflexive differentials enjoy good pull-back properties. A natural generalization of the well-known Bogomolov–Sommese vanishing theorem to log canonical threefold pairs follows.

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