563 research outputs found
The implicit equation of a multigraded hypersurface
In this article we analyze the implicitization problem of the image of a
rational map , with a toric variety of dimension
defined by its Cox ring . Let be homogeneous
elements of . We blow-up the base locus of , , and we
approximate the Rees algebra of this blow-up by the symmetric
algebra . We provide under suitable assumptions, resolutions
for graded by the torus-invariant divisor group of , ,
such that the determinant of a graded strand, , gives a
multiple of the implicit equation, for suitable . Indeed, we
compute a region in which depends on the regularity of where
to choose . We also give a geometrical interpretation of the possible
other factors appearing in . A very detailed description is
given when is a multiprojective space.Comment: 19 pages, 2 figures. To appear in Journal of Algebr
Compactifications of rational maps, and the implicit equations of their images
In this paper we give different compactifications for the domain and the
codomain of an affine rational map which parametrizes a hypersurface. We
show that the closure of the image of this map (with possibly some other extra
hypersurfaces) can be represented by a matrix of linear syzygies. We compactify
into an -dimensional projective arithmetically
Cohen-Macaulay subscheme of some . One particular interesting
compactification of is the toric variety associated to the
Newton polytope of the polynomials defining . We consider two different
compactifications for the codomain of : and .
In both cases we give sufficient conditions, in terms of the nature of the base
locus of the map, for getting a matrix representation of its closed image,
without involving extra hypersurfaces. This constitutes a direct generalization
of the corresponding results established in [BuseJouanolou03],
[BuseChardinJouanolou06], [BuseDohm07], [BotbolDickensteinDohm09] and
[Botbol09].Comment: 2 images, 28 pages. To appear in Journal of Pure and Applied Algebr
Implicitization of rational maps
Motivated by the interest in computing explicit formulas for resultants and
discriminants initiated by B\'ezout, Cayley and Sylvester in the eighteenth and
nineteenth centuries, and emphasized in the latest years due to the increase of
computing power, we focus on the implicitization of hypersurfaces in several
contexts. Our approach is based on the use of linear syzygies by means of
approximation complexes, following [Bus\'e Jouanolou 03], where they develop
the theory for a rational map . Approximation
complexes were first introduced by Herzog, Simis and Vasconcelos in [Herzog
Simis Vasconcelos 82] almost 30 years ago. The main obstruction for this
approximation complex-based method comes from the bad behavior of the base
locus of . Thus, it is natural to try different compatifications of
, that are better suited to the map , in order to avoid unwanted
base points. With this purpose, in this thesis we study toric compactifications
for . We provide resolutions for , such that
gives a multiple of the implicit equation, for a graded strand
. Precisely, we give specific bounds on all these settings
which depend on the regularity of \SIA. Starting from the homogeneous
structure of the Cox ring of a toric variety, graded by the divisor class group
of , we give a general definition of Castelnuovo-Mumford regularity for a
polynomial ring over a commutative ring , graded by a finitely generated
abelian group , in terms of the support of some local cohomology modules. As
in the standard case, for a -graded -module and an homogeneous ideal
of , we relate the support of with the support of
.Comment: PhD. Thesis of the author, from Universit\'e de Paris VI and
Univesidad de Buenos Aires. Advisors: Marc Chardin and Alicia Dickenstein.
Defended the 29th september 2010. 163 pages 15 figure
MS
thesisThe gilsonite and ozokerite deposits of the Unita Basin, Utah, were investigated geochemically. Soil samples were collected along traverses across productive veins in several areas. These soil samples were analysed for gilsonite and ozokerite. The gilsonite and ozokerite content of the soil samples was related to vein proximity. The veins investigated were the Cowboy vein, the Chepetta lode, the Carbon lode, the Rainbow vein, the Pariette vein, and the Soldier Summit ozokerite deposit. Three laboratory procedures were developed to separate gilsonite from the soil samples. All were based on the difference in specific gravity between gilsonite, which has a specific gravity of 1.04, and soil fraction, which has a specific gravity of about 2.0 - 2.6. In one procedure tetrabromoethane in benzene was the heavy liquid medium. In the other procedure carbon tetrachloride was the heavy liquid medium. In each of these procedures, the gilsonite was floated. In the third procedure, the gilsonite was separated from the soil by panning. In each procedure the gilsonite fraction was weighed, and the gilsonite content of each sample was expressed as parts gilsonite per million parts of sample by weight. The precision of the procedures was determined by replicate analyses. The standard deviation of the derived result in the calculation for PPM gilsonite is +-16.6%. Geochemical anomalies were recognized in each instance. Background values ranged from 200 PPM to 1,000 PPM. Anomalies ranged from 2,910 PPM to 264,000 PPM, and the contrast raged from 16 t0 545. In addition to geochemical anomalies disclosed over each vein, several anomalies at a distance from known veins were observed. These anomalies may reflect covered veins. Gilsonite content and dispersion halos surrounding the veins are due to weathering and erosion of gilsonite veins
Maladie de Lyme, syndrome autistique et traitement antibiotique : une réflexion à partir d'un cas
International audienceFollowing an overview of the definition of autism and Lyme disease, a clinical case will be presented of a young subject (aged 14 years and a half) diagnosed with autism, and characterized by a typical development in the first year of life, followed by a general deterioration of abilities shortly after diagnosis of the onset of Lyme disease. The subject presented positive reactivity for Mycoplasma Pneumoniae. According to recent studies, misdiagnosis of initial symptoms of Lyme disease and delayed treatment can lead to persistent interactive coinfections in the organism which may result in chronic pathologies. Thus, a link could exist between a chronic infectionwith Mycoplasma Pneumoniae and an atypical symptomology similar to autism. So the hypothesis proposed is that there may be a correlation between Lyme disease and autism and that long-term antibiotic therapy may be an effective treatment. Following a clinical presentation of the history of this young patient, the evolution of the subject's symptomology and behavior during one year of antibiotic therapy will be described.A la suite d'un rappel de la définition de l'autisme infantile et de la maladie de Lyme, un cas clinique sera développé. Il s'agit d'un jeune patient avec autisme ùgé de 14 ans et demi, caractérisé par un développement initial typique pendant sa premiÚre année puis par une dégradation générale de ses aptitudes peu aprÚs avoir été atteint de la maladie de Lyme. A la suite d'une présentation sous la forme d'une vignette clinique, nous aborderons l'évolution de la symptomatologie et du comportement de ce jeune pendant un an d'antibiothérapie. Cette présentation de cas permettra finalement d'interroger la définition de l'autisme, son étiologie et la validité du diagnostic établi initialement pour ce patient
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