𝔸-curves on log smooth varieties

2019 ◽  
Vol 2019 (756) ◽  
pp. 1-35
Author(s):  
Qile Chen ◽  
Yi Zhu
Keyword(s):  
Homogeneous Spaces ◽  
Projective Spaces ◽  
Point Of View ◽  
Affine Spaces ◽  
Ample Divisors

AbstractIn this paper, we study {\mathbb{A}^{1}}-connected varieties from log geometry point of view, and prove a criterion for {\mathbb{A}^{1}}-connectedness. As applications, we provide many interesting examples of {\mathbb{A}^{1}}-connected varieties in the case of complements of ample divisors, and the case of homogeneous spaces. We also obtain a logarithmic version of Hartshorne conjecture characterizing projective spaces and affine spaces.

scholarly journals Contact metric manifolds with large automorphism group and (κ, µ)-spaces

2019 ◽  
Vol 6 (1) ◽  
pp. 294-302 ◽  
Author(s):  
Antonio Lotta
Keyword(s):  
Automorphism Group ◽  
Symmetric Operator ◽  
Homogeneous Spaces ◽  
Point Of View ◽  
Maximum Dimension ◽  
Contact Metric Manifold ◽  
Contact Metric Manifolds ◽  
Large Automorphism Group ◽  
Dimension 2 ◽  
Simply Connected

AbstractWe discuss the classifiation of simply connected, complete (κ, µ)-spaces from the point of view of homogeneous spaces. In particular, we exhibit new models of (κ, µ)-spaces having Boeckx invariant -1. Finally, we prove that the number ${{(n + 1)(n + 2)} \over 2}$ is the maximum dimension of the automorphism group of a contact metric manifold of dimension 2n +1, n ≥ 2, whose symmetric operator h has rank at least 3 at some point; if this dimension is attained, and the dimension of the manifold is not 7, it must be a (κ, µ)-space. The same conclusion holds also in dimension 7 provided the almost CR structure of the contact metric manifold under consideration is integrable.

scholarly journals On the cohomology of loop spaces of compact Lie groups

1985 ◽  
Vol 26 (1) ◽  
pp. 91-99 ◽  
Author(s):  
Howard Hiller
Keyword(s):  
Homogeneous Spaces ◽  
Cell Decomposition ◽  
Point Of View ◽  
Loop Spaces ◽  
Bruhat Decomposition ◽  
Infinite Dimensional ◽  
Dimensional Group ◽  
Analogous Question ◽  
A Cell ◽  
Simply Connected

Let G be a compact, simply-connected Lie group. The cohomology of the loop space ΏG has been described by Bott, both in terms of a cell decomposition [1] and certain homogeneous spaces called generating varieties [2]. It is possible to view ΏG as an infinite dimensional “Grassmannian” associated to an appropriate infinite dimensional group, cf. [3], [7]. From this point of view the above cell-decomposition of Bott arises from a Bruhat decomposition of the associated group. We choose a generator H ∈ H2(ΏG, ℤ) and call it the hyperplane class. For a finite-dimensional Grassmannian the highest power of H carries geometric information about the variety, namely, its degree. An analogous question for ΏG is: What is the largest integer Nk = Nk(G) which divides Hk ∈ H2k(ΏG, ℤ)?Of course, if G = SU(2) = S3, one knows Nk = h!. In general, the deviation of Nk from k! measures the failure of H to generate a divided polynomial algebra in H*(ΏG, ℤ).

scholarly journals Affine Spaces within Projective Spaces

1999 ◽  
Vol 36 (3-4) ◽  
pp. 237-251 ◽  
Author(s):  
Andrea Blunck ◽  
Hans Havlicek
Keyword(s):  
Projective Spaces ◽  
Affine Spaces

INDUCED REPRESENTATIONS, GAUGE FIELDS, AND QUANTIZATION ON HOMOGENEOUS SPACES

1992 ◽  
Vol 04 (04) ◽  
pp. 503-527 ◽  
Author(s):  
N.P. LANDSMAN
Keyword(s):  
Homogeneous Spaces ◽  
Quantum Particle ◽  
Classical Field Theory ◽  
Geometric Realization ◽  
Point Of View ◽  
Classical Particle ◽  
Moment Maps ◽  
Enveloping Algebra ◽  
Casimir Operators ◽  
Lie Subgroup

We study representations of the enveloping algebra of a Lie group G which are induced by a representation of a Lie subgroup H, assuming that G/H is reductive. Such representations describe the superselection sectors of a quantum particle moving on G/H. It is found that the representatives of both the generators and the quadratic Casimir operators of G have a natural geometric realization in terms of the canonical connection on the principal H-bundle G. The explicit expression for the generators can be understood from the point of view of conservation laws and moment maps in classical field theory and classical particle mechanics on G/H. The emergence of classical geometric structures in the quantum-mechanical situation is explained by a detailed study of the domain and possible self-adjointness properties of the relevant operators. A new and practical criterion for essential self-adjointness in general unitary representations is given.

scholarly journals CHARACTERIZATION OF PROJECTIVE SPACES AND -BUNDLES AS AMPLE DIVISORS

2017 ◽  
Vol 233 ◽  
pp. 155-169 ◽  
Author(s):  
JIE LIU
Keyword(s):  
Recent Work ◽  
Projective Spaces ◽  
Ample Divisor ◽  
Projective Manifold ◽  
Projective Manifolds ◽  
Ample Divisors

Let $X$ be a projective manifold of dimension $n$. Suppose that $T_{X}$ contains an ample subsheaf. We show that $X$ is isomorphic to $\mathbb{P}^{n}$. As an application, we derive the classification of projective manifolds containing a $\mathbb{P}^{r}$-bundle as an ample divisor by the recent work of Litt.

scholarly journals On Sets with Few Intersection Numbers in Finite Projective and Affine Spaces

10.37236/3434 ◽  
2014 ◽  
Vol 21 (4) ◽  
Author(s):  
Nicola Durante
Keyword(s):  
Projective Spaces ◽  
Galois Field ◽  
Constant Number ◽  
Intersection Numbers ◽  
Main Motivation ◽  
Affine Spaces ◽  
Maximal Arc ◽  
Johnson Graphs ◽  
Projective And Affine Spaces

In this paper we study sets $X$ of points of both affine and projective spaces over the Galois field $\mathop{\rm{GF}}(q)$ such that every line of the geometry that is neither contained in $X$ nor disjoint from $X$ meets the set $X$ in a constant number of points and we determine all such sets. This study has its main motivation in connection with a recent study of neighbour transitive codes in Johnson graphs by Liebler and Praeger [Designs, Codes and Crypt., 2014]. We prove that, up to complements, in $\mathop{\rm{PG}}(n,q)$ such a set $X$ is either a subspace or $n=2,q$ is even and $X$ is a maximal arc of degree $m$. In $\mathop{\rm{AG}}(n,q)$ we show that $X$ is either the union of parallel hyperplanes or a cylinder with base a maximal arc of degree $m$ (or the complement of a maximal arc) or a cylinder with base the projection of a quadric. Finally we show that in the affine case there are examples (different from subspaces or their complements) in $\mathop{\rm{AG}}(n,4)$ and in $\mathop{\rm{AG}}(n,16)$ giving new neighbour transitive codes in Johnson graphs.

The Geosciences Applied to Lunar Exploration

1962 ◽  
Vol 14 ◽  
pp. 169-257 ◽  
Author(s):  
J. Green
Keyword(s):  
Lunar Surface ◽  
Probable Mechanism ◽  
Point Of View ◽  
Lunar Exploration ◽  
Geological Model ◽  
Apply Geophysics ◽  
Surface Features ◽  
The Impact

The term geo-sciences has been used here to include the disciplines geology, geophysics and geochemistry. However, in order to apply geophysics and geochemistry effectively one must begin with a geological model. Therefore, the science of geology should be used as the basis for lunar exploration. From an astronomical point of view, a lunar terrain heavily impacted with meteors appears the more reasonable; although from a geological standpoint, volcanism seems the more probable mechanism. A surface liberally marked with volcanic features has been advocated by such geologists as Bülow, Dana, Suess, von Wolff, Shaler, Spurr, and Kuno. In this paper, both the impact and volcanic hypotheses are considered in the application of the geo-sciences to manned lunar exploration. However, more emphasis is placed on the volcanic, or more correctly the defluidization, hypothesis to account for lunar surface features.

How a sheperd guides a sheep herd?

1984 ◽  
Vol 75 ◽  
pp. 331-337
Author(s):  
Richard Greenberg
Keyword(s):  
Point Of View ◽  
Single Ring ◽  
Damping Effects ◽  
Ring Particle

ABSTRACTThe mechanism by which a shepherd satellite exerts a confining torque on a ring is considered from the point of view of a single ring particle. It is still not clear how one might most meaningfully include damping effects and other collisional processes into this type of approach to the problem.

The growth of mica polytypes as studied by conventional and high-resolution TEM

1983 ◽  
Vol 41 ◽  
pp. 174-177
Author(s):  
A. Baronnet ◽  
M. Amouric
Keyword(s):  
Water Pressure ◽  
Point Of View ◽  
Temperature Fields ◽  
Natural Occurrence ◽  
Growth Mechanisms ◽  
Long Period ◽  
High Resolution Tem ◽  
Layer Stacking ◽  
Experimental Works ◽  
Potential Use

The origin of mica polytypes has long been a challenging problem for crystal- lographers, mineralogists and petrologists. From the petrological point of view, interest in this field arose from the potential use of layer stacking data to furnish further informations about equilibrium and/or kinetic conditions prevailing during the crystallization of the widespread mica-bearing rocks. From the compilation of previous experimental works dealing with the occurrence domains of the various mica "polymorphs" (1Mr, 1M, 2M1, 2M2 and 3T) within water-pressure vs temperature fields, it became clear that most of these modifications should be considered as metastable for a fixed mica species. Furthermore, the natural occurrence of long-period (or complex) polytypes could not be accounted for by phase considerations. This highlighted the need of a more detailed kinetic approach of the problem and, in particular, of the role growth mechanisms of basal faces could play in this crystallographic phenomenon.

Radiation Damage in Ceramics

1982 ◽  
Vol 40 ◽  
pp. 600-603
Author(s):  
T. E. Mitchell ◽  
M. R. Pascucci ◽  
R. A. Youngman
Keyword(s):  
Radiation Damage ◽  
Outer Space ◽  
Point Of View ◽  
Nuclear Waste Storage ◽  
Waste Storage ◽  
Storage Media ◽  
Transmission Electron ◽  
Fundamental Point ◽  
Small Defect ◽  
Present Understanding

1. Introduction. Studies of radiation damage in ceramics are of interest not only from a fundamental point of view but also because it is important to understand the behavior of ceramics in various practical radiation enyironments- fission and fusion reactors, nuclear waste storage media, ion-implantation devices, outer space, etc. A great deal of work has been done on the spectroscopy of point defects and small defect clusters in ceramics, but relatively little has been performed on defect agglomeration using transmission electron microscopy (TEM) in the same kind of detail that has been so successful in metals. This article will assess our present understanding of radiation damage in ceramics with illustrations using results obtained from the authors' work.

Sign in / Sign up

Export Citation Format

Share Document