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Gorenstein liaison of some curves in P4.

Joshua Lesperance (2001)

Collectanea Mathematica

Despite the recent advances made in Gorenstein liaison, there are still many open questions for the theory in codimension ≥ 3. In particular we consider the following question: given two curves in Pn with isomorphic deficiency modules (up to shift), can they be evenly Gorenstein linked? The answer for this is yes for curves in P3, due to Rao, but for higher codimension the answer is not known. This paper will look at large classes of curves in P4 with isomorphic deficiency modules and show that...

Groupe de Brauer non ramifié d’espaces homogènes de tores

Jean-Louis Colliot-Thélène (2014)

Journal de Théorie des Nombres de Bordeaux

Soient k un corps et X une k -variété projective et lisse. Si X est géométriquement rationnelle, on dispose d’une application injective du quotient de groupes de Brauer Br ( X ) / Br ( k ) dans le premier groupe de cohomologie galoisienne du réseau défini par le groupe de Picard géométrique de X . Dans cette note on donne des cas où cette application est toujours surjective. Pour les espaces homogènes de certains tores algébriques, on donne des générateurs explicites dans Br ( X ) . On applique cela à l’étude du principe de...

Heights of varieties in multiprojective spaces and arithmetic Nullstellensätze

Carlos D’Andrea, Teresa Krick, Martín Sombra (2013)

Annales scientifiques de l'École Normale Supérieure

We present bounds for the degree and the height of the polynomials arising in some problems in effective algebraic geometry including the implicitization of rational maps and the effective Nullstellensatz over a variety. Our treatment is based on arithmetic intersection theory in products of projective spaces and extends to the arithmetic setting constructions and results due to Jelonek. A key role is played by the notion of canonical mixed height of a multiprojective variety. We study this notion...

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