557 research outputs found
A sufficient condition for a number to be the order of a nonsingular derivation of a Lie algebra
A study of the set N_p of positive integers which occur as orders of
nonsingular derivations of finite-dimensional non-nilpotent Lie algebras of
characteristic p>0 was initiated by Shalev and continued by the present author.
The main goal of this paper is to show the abundance of elements of N_p. Our
main result shows that any divisor n of q-1, where q is a power of p, such that
, belongs to N_p. This extends its special
case for p=2 which was proved in a previous paper by a different method.Comment: 10 pages. This version has been revised according to a referee's
suggestions. The additions include a discussion of the (lower) density of the
set N_p, and the results of more extensive machine computations. Note that
the title has also changed. To appear in Israel J. Mat
A simple remark on a flat projective morphism with a Calabi-Yau fiber
If a K3 surface is a fiber of a flat projective morphisms over a connected
noetherian scheme over the complex number field, then any smooth connected
fiber is also a K3 surface. Observing this, Professor Nam-Hoon Lee asked if the
same is true for higher dimensional Calabi-Yau fibers. We shall give an
explicit negative answer to his question as well as a proof of his initial
observation.Comment: 8 pages, main theorem is generalized, one more remark is added,
mis-calculation and typos are corrected etc
Semipurity of tempered Deligne cohomology
In this paper we define the formal and tempered Deligne cohomology groups,
that are obtained by applying the Deligne complex functor to the complexes of
formal differential forms and tempered currents respectively. We then prove the
existence of a duality between them, a vanishing theorem for the former and a
semipurity property for the latter. The motivation of these results comes from
the study of covariant arithmetic Chow groups. The semi-purity property of
tempered Deligne cohomology implies, in particular, that several definitions of
covariant arithmetic Chow groups agree for projective arithmetic varieties
On the classification of Kahler-Ricci solitons on Gorenstein del Pezzo surfaces
We give a classification of all pairs (X,v) of Gorenstein del Pezzo surfaces
X and vector fields v which are K-stable in the sense of Berman-Nystrom and
therefore are expected to admit a Kahler-Ricci solition. Moreover, we provide
some new examples of Fano threefolds admitting a Kahler-Ricci soliton.Comment: 21 pages, ancillary files containing calculations in SageMath; minor
correction
Generating multimedia presentations: from plain text to screenplay
In many Natural Language Generation (NLG) applications, the output is limited to plain text – i.e., a string of words with punctuation and paragraph breaks, but no indications for layout, or pictures, or dialogue. In several projects, we have begun to explore NLG applications in which these extra media are brought into play. This paper gives an informal account of what we have learned. For coherence, we focus on the domain of patient information leaflets, and follow an example in which the same content is expressed first in plain text, then in formatted text, then in text with pictures, and finally in a dialogue script that can be performed by two animated agents. We show how the same meaning can be mapped to realisation patterns in different media, and how the expanded options for expressing meaning are related to the perceived style and tone of the presentation. Throughout, we stress that the extra media are not simple added to plain text, but integrated with it: thus the use of formatting, or pictures, or dialogue, may require radical rewording of the text itself
Affine T-varieties of complexity one and locally nilpotent derivations
Let X=spec A be a normal affine variety over an algebraically closed field k
of characteristic 0 endowed with an effective action of a torus T of dimension
n. Let also D be a homogeneous locally nilpotent derivation on the normal
affine Z^n-graded domain A, so that D generates a k_+-action on X that is
normalized by the T-action. We provide a complete classification of pairs (X,D)
in two cases: for toric varieties (n=\dim X) and in the case where n=\dim X-1.
This generalizes previously known results for surfaces due to Flenner and
Zaidenberg. As an application we compute the homogeneous Makar-Limanov
invariant of such varieties. In particular we exhibit a family of non-rational
varieties with trivial Makar-Limanov invariant.Comment: 31 pages. Minor changes in the structure. Fixed some typo
On localization in holomorphic equivariant cohomology
We prove a localization formula for a "holomorphic equivariant cohomology"
attached to the Atiyah algebroid of an equivariant holomorphic vector bundle.
This generalizes Feng-Ma, Carrell-Liebermann, Baum-Bott and K. Liu's
localization formulas.Comment: 16 pages. Completely rewritten, new title. v3: Minor changes in the
exposition. v4: final version to appear in Centr. Eur. J. Mat
The Neron-Severi group of a proper seminormal complex variety
We prove a Lefschetz (1,1)-Theorem for proper seminormal varieties over the
complex numbers. The proof is a non-trivial geometric argument applied to the
isogeny class of the Lefschetz 1-motive associated to the mixed Hodge structure
on H^2.Comment: 16 pages; Mathematische Zeitschrift (2008
On rationality of the intersection points of a line with a plane quartic
We study the rationality of the intersection points of certain lines and
smooth plane quartics C defined over F_q. For q \geq 127, we prove the
existence of a line such that the intersection points with C are all rational.
Using another approach, we further prove the existence of a tangent line with
the same property as soon as the characteristic of F_q is different from 2 and
q \geq 66^2+1. Finally, we study the probability of the existence of a rational
flex on C and exhibit a curious behavior when the characteristic of F_q is
equal to 3.Comment: 17 pages. Theorem 2 now includes the characteristic 2 case;
Conjecture 1 from the previous version is proved wron
Relativistic nature of a magnetoelectric modulus of Cr_2O_3-crystals: a new 4-dimensional pseudoscalar and its measurement
Earlier, the magnetoelectric effect of chromium sesquioxide Cr_2O_3 has been
determined experimentally as a function of temperature. One measures the
electric field-induced magnetization on Cr_2O_3 crystals or the magnetic
field-induced polarization. From the magnetoelectric moduli of Cr_2O_3 we
extract a 4-dimensional relativistic invariant pseudoscalar
. It is temperature dependent and of the order of
10^{-4}/Z_0, with Z_0 as vacuum impedance. We show that the new pseudoscalar is
odd under parity transformation and odd under time inversion. Moreover,
is for Cr_2O_3 what Tellegen's gyrator is for two port
theory, the axion field for axion electrodynamics, and the PEMC (perfect
electromagnetic conductor) for electrical engineering.Comment: Revtex, 36 pages, 9 figures (submitted in low resolution, better
quality figures are available from the authors
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