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Seshadri positive curves in a smooth projective 3 -fold

Roberto Paoletti (1995)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

A notion of positivity, called Seshadri ampleness, is introduced for a smooth curve C in a polarized smooth projective 3 -fold X , A , whose motivation stems from some recent results concerning the gonality of space curves and the behaviour of stable bundles on P 3 under restriction to C . This condition is stronger than the normality of the normal bundle and more general than C being defined by a regular section of an ample rank- 2 vector bundle. We then explore some of the properties of Seshadri-ample curves....

Some examples of Gorenstein liaison in codimension three.

Robin Hartshorne (2002)

Collectanea Mathematica

Gorenstein liaison seems to be the natural notion to generalize to higher codimension the well-known results about liaison of varieties of codimension 2 in projective space. In this paper we study points in P3 and curves in P4 in an attempt to see how far typical codimension 2 results will extend. While the results are satisfactory for small degree, we find in each case examples where we cannot decide the outcome. This examples are candidates for counterexamples to the hoped-for extensions of codimension...

Subcanonicity of codimension two subvarieties.

Enrique Arrondo (2005)

Revista Matemática Complutense

We prove that smooth subvarieties of codimension two in Grassmannians of lines of dimension at least six are rationally numerically subcanonical. We prove the same result for smooth quadrics of dimension at least six under some extra condition. The method is quite easy, and only uses Serre s construction, Porteous formula, and Hodge index theorem.

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