5,918 research outputs found
Vanishing via lifting to second Witt vectors and a proof of an isotriviality result
A proof based on reduction to finite fields of Esnault-Viehweg's stronger
version of Sommese Vanishing Theorem for -ample line bundles is given. This
result is used to give different proofs of isotriviality results of A. Parshin
and L. Migliorini.Comment: Latex, 7 page
Effective nonvanishing, effective global generation
We prove a multiple-points higher-jets nonvanishing theorem by the use of
local Seshadri constants. Applications are given to effectivity problems such
as constructing rational and birational maps into Grassmannians, and the global
generation of vector bundles.Comment: LaTex (article) 13 pages; revised: one section added; to appear in
Ann. Inst. Fourie
Singular hermitian metrics on vector bundles
We introduce a notion of singular hermitian metrics (s.h.m.) for holomorphic
vector bundles and define positivity in view of -estimates. Associated
with a suitably positive s.h.m. there is a (coherent) sheaf 0-th kernel of a
certain -complex. We prove a vanishing theorem for the cohomology of this
sheaf. All this generalizes to the case of higher rank known results of Nadel
for the case of line bundles. We introduce a new semi-positivity notion,
-nefness, for vector bundles, establish some of its basic properties and
prove that on curves it coincides with ordinary nefness. We particularize the
results on s.h.m. to the case of vector bundles of the form ,
where is a -nef vector bundle and is a positive (in the sense of
currents) line bundle. As applications we generalize to the higher rank case 1)
Kawamata-Viehweg Vanishing Theorem, 2) the effective results concerning the
global generation of jets for the adjoint to powers of ample line bundles, and
3) Matsusaka Big Theorem made effective.Comment: LaTex (article) 25 pages; revised: minor changes; to appear in
Crelle's J; dedicated to Michael Schneide
Radiation in (2+1)-dimensions
In this paper we discuss the radiation equation of state in
(2+1)-dimensions. In (3+1)-dimensions the equation of state may be
used to describe either actual electromagnetic radiation (photons) as well as a
gas of massless particles in a thermodynamic equilibrium (for example
neutrinos). In this work it is shown that in the framework of (2+1)-dimensional
Maxwell electrodynamics the radiation law takes place only for plane
waves, i.e. for . Instead of the linear Maxwell electrodynamics, to
derive the (2+1)-radiation law for more general cases with , one has
to use a conformally invariant electrodynamics, which is a 2+1-nonlinear
electrodynamics with a trace free energy-momentum tensor, and to perform a
volumetric spatial average of the corresponding Maxwell stress-energy tensor
with its electric and magnetic components at a given instant of time .Comment: 7 pages. Accepted for publication in Phys. Lett.
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