65,431 research outputs found
Embeddings of homogeneous spaces in prime characteristics
Let be a reductive linear algebraic group. The simplest example of a
projective homogeneous -variety in characteristic , not isomorphic to a
flag variety, is the divisor in , which is modulo a non-reduced stabilizer containing the upper
triangular matrices. In this paper embeddings of projective homogeneous spaces
viewed as , where is any subgroup scheme containing a Borel subgroup,
are studied. We prove that can be identified with the orbit of the
highest weight line in the projective space over the simple -representation
of a certain highest weight . This leads to some strange
embeddings especially in characteristic , where we give an example in the
-case lying on the boundary of Hartshorne's conjecture on complete
intersections. Finally we prove that ample line bundles on are very
ample. This gives a counterexample to Kodaira type vanishing with a very ample
line bundle, answering an old question of Raynaud.Comment: 10 pages, AMS-LaTe
Adding fuel to the flames: how TTIP reinvigorated the politicization of trade
It is a truism to state that the Transatlantic Trade and Investment Partnership (TTIP) is a politicized issue, yet the explanations that account for this politicization are mostly singular in nature. In this paper I add to this understanding theoretically and empirically by presenting a broad analytic framework that puts TTIP at the intersection of two evolutions. There is, firstly, a longer-term trend of increasing political authority of (European) trade policy that is (at least by several organizations and citizens) not considered legitimate. I argue that TTIP is an extension and an intensification of this perceived authority-without-legitimacy trend. Secondly, the particular explosive situation that has occurred since 2013 is furthermore the result of a specific combination of a favoring political opportunity structure, combined with pre-existing mobilization resources that have facilitated a large mobilization by civil society organizations. This explains the spike of politicization that is attached onto this longer term trend. Relying on several exploratory interviews, I try to uncover the determinants in the different categories
Batalin-Vilkovisky algebra structures on (Co)Tor and Poisson bialgebroids
In this article, we extend our preceding studies on higher algebraic
structures of (co)homology theories defined by a left bialgebroid (U,A). For a
braided commutative Yetter-Drinfel'd algebra N, explicit expressions for the
canonical Gerstenhaber algebra structure on Ext_U(A,N) are given. Similarly, if
(U,A) is a left Hopf algebroid where A is an anti Yetter-Drinfel'd module over
U, it is shown that the cochain complex computing Cotor_U(A,N) defines a cyclic
operad with multiplication and hence the groups Cotor_U(A,N) form a
Batalin-Vilkovisky algebra. In the second part of this article, Poisson
structures and the Poisson bicomplex for bialgebroids are introduced, which
simultaneously generalise, for example, classical Poisson as well as cyclic
homology. In case the bialgebroid U is commutative, a Poisson structure on U
leads to a Batalin-Vilkovisky algebra structure on Tor_U(A,A). As an
illustration, we show how this generalises the classical Koszul bracket on
differential forms, and conclude by indicating how classical Lie-Rinehart
bialgebras (or, geometrically, Lie bialgebroids) arise from left bialgebroids.Comment: 37 pages; minor revision (v3: added table of contents), to appear in
J. Pure Appl. Algebr
Farming the future
The sustainable production of high quality food, reducing dependency on high energy inputs, improving environmentaland nature conservation, climate change adaptation, animalwelfare and rural livelihoods, are all important challenges faced byEuropean agriculture which can be addressed through organicagricultural practices.
However, while the sector has grown dramatically in recent times,much more research needs to be done for this innovative field to come to realise its true potential. As such, the CORE Organic II ERA-Net aims at an effective and sustainable transnational researchprogramme, and has identified common research priorities for the organic sector where a transnational approach will give added value, has initiated research projects, and is organising project monitoring and the dissemination of results.
PEN asked Dr Niels Halberg, director of the International Centre for Research in Organic Food Systems (ICROFS) and co-ordinator of the CORE Organic II ERA-Net about the benefits the initiative can bring, the project selection process, and his views on the future of organic agriculture research funding, both at a European and national level
Deriving the Gross-Pitaevskii equation
In experiments, Bose-Einstein condensates are prepared by cooling a dilute
Bose gas in a trap. After the phase transition has been reached, the trap is
switched off and the evolution of the condensate observed. The evolution is
macroscopically described by the Gross-Pitaevskii equation. On the microscopic
level, the dynamics of Bose gases are described by the -body Schr\"odinger
equation. We review our article [BdS12] in which we construct a class of
initial data in Fock space which are energetically close to the ground state
and prove that their evolution approximately follows the Gross-Pitaevskii
equation. The key idea is to model two-particle correlations with a Bogoliubov
transformation.Comment: 5 pages; contribution to the proceedings of QMath1
Density of quasismooth hypersurfaces in simplicial toric varieties
This paper investigates the density of hypersurfaces in a projective normal
simplicial toric variety over a finite field having a quasismooth intersection
with a given quasismooth subscheme. The result generalizes the formula found by
B. Poonen for smooth projective varieties. As an application, we further
analyze the density of hypersurfaces with bounds on their number of
singularities and on the length of their singular schemes.Comment: extended and accepted versio
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