scholarly journals ALGEBRAIC FOLIATIONS DEFINED BY QUASI-LINES

2011 ◽  
Vol 22 (10) ◽  
pp. 1501-1528
Author(s):  
LAURENT BONAVERO ◽  
ANDREAS HÖRING
Keyword(s):  
Projective Space ◽  
Singular Locus ◽  
Projective Manifold ◽  
Line Passing ◽  
Rational Fibration ◽  
Algebraic Foliations

Let X be a projective manifold containing a quasi-line l. An important difference between quasi-lines and lines in the projective space is that in general there is more than one quasi-line passing through two given general points. In this paper, we use this feature to construct an algebraic foliation associated to a family of quasi-lines. We prove that if the singular locus of this foliation is not too large, it induces a rational fibration on X that maps the general leaf of the foliation onto a quasi-line in a rational variety.

REAL PROJECTIVE MANIFOLDS DEVELOPING INTO AN AFFINE SPACE

1993 ◽  
Vol 04 (02) ◽  
pp. 179-191 ◽  
Author(s):  
YOUNKI CHAE ◽  
SUHYOUNG CHOI ◽  
CHAN-YOUNG PARK
Keyword(s):  
Projective Space ◽  
Affine Space ◽  
Dimensional Subspace ◽  
Affine Group ◽  
Projective Manifold ◽  
Hilbert Metric ◽  
Projective Manifolds

Suppose that an n-dimensional closed real projective manifold M, n ≥ 2, develops into an affine space RPn − RPn − 1 for an (n − 1)-dimensional subspace RPn − 1 of the projective space RPn. Then either M is convex or affine or M admits a flat foliation [Formula: see text] with a transverse invariant Hilbert metric. Further, if the codimension of [Formula: see text] is n − 1, then M is convex. We prove this statement by a use of a variation of Carrière's discompacté, a measure of non-compactedness of an affine group acting on an affine space.

scholarly journals Higher codimensional foliations with Kupka singularities

2017 ◽  
Vol 28 (03) ◽  
pp. 1750019
Author(s):  
O. Calvo-Andrade ◽  
M. Corrêa ◽  
A. Fernández-Pérez
Keyword(s):  
Normal Form ◽  
Positive Integer ◽  
Projective Space ◽  
Complete Intersection ◽  
Holomorphic Foliations ◽  
Connected Component ◽  
Codimension One ◽  
Dimension Formula ◽  
Rational Fibration

We consider holomorphic foliations of dimension [Formula: see text] and codimension [Formula: see text] in the projective space [Formula: see text], with a compact connected component of the Kupka set. We prove that if the transversal type is linear with positive integer eigenvalues, then the foliation consists of the fibers of a rational fibration [Formula: see text]. As a corollary, if [Formula: see text] and has a transversal type diagonal with different eigenvalues, then the Kupka component [Formula: see text] is a complete intersection and the leaves of the foliation define a rational fibration. The same conclusion holds if the Kupka set has a radial transversal type. Finally, as an application, we find a normal form for non-integrable codimension-one distributions on [Formula: see text].

scholarly journals Singular loci of instanton sheaves on projective space

2016 ◽  
Vol 27 (07) ◽  
pp. 1640006 ◽  
Author(s):  
Michael Gargate ◽  
Marcos Jardim
Keyword(s):  
Projective Space ◽  
Singular Locus ◽  
Dimension Formula ◽  
Pure Dimension ◽  
Singular Loci ◽  
Higher Rank

We prove that the singular locus of a rank [Formula: see text] non-locally free instanton sheaf [Formula: see text] on [Formula: see text] has pure dimension [Formula: see text]. Moreover, we also show that the dual and double dual of [Formula: see text] are isomorphic locally free instanton sheaves, and that the sheaves [Formula: see text] and [Formula: see text] are rank [Formula: see text] instantons. We also provide explicit examples of instanton sheaves of ranks [Formula: see text] and [Formula: see text] illustrating that all of these claims are false for higher rank instanton sheaves.

scholarly journals Deformations of the tangent bundle of projective manifolds

2020 ◽  
Vol 31 (11) ◽  
pp. 2050087
Author(s):  
Thomas Peternell
Keyword(s):  
Projective Space ◽  
Tangent Bundle ◽  
Complex Projective Space ◽  
Projective Manifold ◽  
First Order ◽  
Projective Manifolds ◽  
Complex Projective

We investigate when the tangent bundle of a projective manifold has a nontrivial first-order (or positive-dimensional) deformation. This leads to a new conjectural characterization of the complex projective space.

Development and testing of rolling cutter bit with a new arrangement of teeth on the balls

2020 ◽  
pp. 60-68
Author(s):  
V. A. Pyalchenkov ◽  
D. V. Pyalchenkov
Keyword(s):  
Axial Force ◽  
Axial Load ◽  
Vertical Line ◽  
Ball Joint ◽  
Line Passing

Research has found that the axial load applied to the bit is distributed unevenly along the crowns of the balls. The middle crowns are the busiest. The value of the axial force perceived by a separate ring is associated with the deformation of the details of the ball joint. You can reduce the uneven loading of crowns by shifting them along the ball along the radius of the bit, placing them so that the vertical line passing through the center of the lower ball of the lock bearing passes through the middle of the gap between the crowns of neighboring balls. The bits with the new option of placing the teeth on the balls were tested on the stand and in industrial conditions. For the bits of this design, the axial load was distributed more evenly over the crowns, which allowed increasing the efficiency of their work.

scholarly journals Towards the classification of rank-r $$ \mathcal{N} $$ = 2 SCFTs. Part I. Twisted partition function and central charge formulae

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Mario Martone
Keyword(s):  
Partition Function ◽  
Central Charge ◽  
Singular Locus ◽  
Companion Paper ◽  
Coulomb Branch ◽  
Energy Limit ◽  
Superconformal Field Theories ◽  
Rank 2 ◽  
Explicit Formulae

Abstract We derive explicit formulae to compute the a and c central charges of four dimensional $$ \mathcal{N} $$ N = 2 superconformal field theories (SCFTs) directly from Coulomb branch related quantities. The formulae apply at arbitrary rank. We also discover general properties of the low-energy limit behavior of the flavor symmetry of $$ \mathcal{N} $$ N = 2 SCFTs which culminate with our $$ \mathcal{N} $$ N = 2 UV-IR simple flavor condition. This is done by determining precisely the relation between the integrand of the partition function of the topologically twisted version of the 4d $$ \mathcal{N} $$ N = 2 SCFTs and the singular locus of their Coulomb branches. The techniques developed here are extensively applied to many rank-2 SCFTs, including new ones, in a companion paper.This manuscript is dedicated to the memory of Rayshard Brooks, George Floyd, Breonna Taylor and the countless black lives taken by US police forces and still awaiting justice. Our hearts are with our colleagues of color who suffer daily the consequences of this racist world.

scholarly journals Embedding Feynman integral (Calabi-Yau) geometries in weighted projective space

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Jacob L. Bourjaily ◽  
Andrew J. McLeod ◽  
Cristian Vergu ◽  
Matthias Volk ◽  
Matt von Hippel ◽  
...  
Keyword(s):  
Projective Space ◽  
Feynman Integral ◽  
Weighted Projective Space

scholarly journals On the set of divisors with zero geometric defect

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Dinh Tuan Huynh ◽  
Duc-Viet Vu
Keyword(s):  
Line Bundle ◽  
Zero Divisor ◽  
Ample Line Bundle ◽  
Holomorphic Section ◽  
Projective Manifold ◽  
Holomorphic Curve ◽  
Very Ample Line Bundle ◽  
Complex Projective ◽  
Geometric Defect

AbstractLet {f:\mathbb{C}\to X} be a transcendental holomorphic curve into a complex projective manifold X. Let L be a very ample line bundle on {X.} Let s be a very generic holomorphic section of L and D the zero divisor given by {s.} We prove that the geometric defect of D (defect of truncation 1) with respect to f is zero. We also prove that f almost misses general enough analytic subsets on X of codimension 2.

Branched Coverings and Minimal Free Resolution for Infinite-Dimensional Complex Spaces

2003 ◽  
Vol 10 (1) ◽  
pp. 37-43
Author(s):  
E. Ballico
Keyword(s):  
Projective Space ◽  
Projective Spaces ◽  
Free Resolution ◽  
Complete Intersections ◽  
Vanishing Theorem ◽  
Sheaf Cohomology ◽  
Minimal Free Resolution ◽  
Branched Coverings ◽  
Infinite Dimensional ◽  
Complex Spaces

Abstract We consider the vanishing problem for higher cohomology groups on certain infinite-dimensional complex spaces: good branched coverings of suitable projective spaces and subvarieties with a finite free resolution in a projective space P(V ) (e.g. complete intersections or cones over finitedimensional projective spaces). In the former case we obtain the vanishing result for H 1. In the latter case the corresponding results are only conditional for sheaf cohomology because we do not have the corresponding vanishing theorem for P(V ).

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