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Linearly Normal Curves in P^n

Pasarescu, Ovidiu (2004)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 14H45, 14H50, 14J26.We construct linearly normal curves covering a big range from P^n, n ≥ 6 (Theorems 1.7, 1.9). The problem of existence of such algebraic curves in P^3 has been solved in [4], and extended to P^4 and P^5 in [10]. In both these papers is used the idea appearing in [4] and consisting in adding hyperplane sections to the curves constructed in [6] (for P^3) and [15, 11] (for P^4 and P^5) on some special surfaces. In the present paper we apply...

Local embeddings of lines in singular hypersurfaces

Guangfeng Jiang, Dirk Siersma (1999)

Annales de l'institut Fourier

Lines on hypersurfaces with isolated singularities are classified. New normal forms of simple singularities with respect to lines are obtained. Several invariants are introduced.

Localisation formelle et groupe de Picard

Jean Fresnel, Marius Van Der Put (1983)

Annales de l'institut Fourier

Soient X un espace analytique affinoïde réduit sur un corps K complet pour une valeur absolue non archimédienne, r : X X ^ sa réduction canonique et p X ^ un point de la variété algébrique affine X ^ . Ce travail décrit la singularité du point p à l’aide d’objets associés à l’espace X : la localisation formelle 𝒪 X , ( p ) qui est une K -algèbre noethérienne de spectre maximal r - 1 ( p ) et dont la réduction est 𝒪 X ^ , ( p )  ; un complété formel 𝒪 X , ( p ) qui est une K -algèbre noethérienne dont la réduction est 𝒪 X ^ , ( p ) . Les résultats essentiels sont obtenus...

Logarithmic Surfaces and Hyperbolicity

Gerd Dethloff, Steven S.-Y. Lu (2007)

Annales de l’institut Fourier

In 1981 J. Noguchi proved that in a logarithmic algebraic manifold, having logarithmic irregularity strictly bigger than its dimension, any entire curve is algebraically degenerate.In the present paper we are interested in the case of manifolds having logarithmic irregularity equal to its dimension. We restrict our attention to Brody curves, for which we resolve the problem completely in dimension 2: in a logarithmic surface with logarithmic irregularity 2 and logarithmic Kodaira dimension 2 , any...

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