A class of non-algebraic threefolds

Matei Toma

Displaying similar documents to “A class of non-algebraic threefolds”

On the cohomological strata of families of vector bundles on algebraic surfaces

Edoardo Ballico (1991)

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

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In this Note we study certain natural subsets of the cohomological stratification of the moduli spaces of rank $2$ vector bundles on an algebraic surface. In the last section we consider the following problem: take a bundle $E$ given by an extension, how can one recognize that $E$ is a certain given bundle? The most interesting case considered here is the case $E = T P^{3} (t)$ since it applies to the study of codimension $1$ meromorphic foliations with singularities on $P^{3}$ .

Holomorphic rank-2 vector bundles on non-Kähler elliptic surfaces

Vasile Brînzănescu, Ruxandra Moraru (2005)

Annales de l’institut Fourier

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In this paper, we consider the problem of determining which topological complex rank-2 vector bundles on non-Kähler elliptic surfaces admit holomorphic structures; in particular, we give necessary and sufficient conditions for the existence of holomorphic rank-2 vector bundles on non-{Kä}hler elliptic surfaces.

Poincaré bundles for projective surfaces

Nicole Mestrano (1985)

Annales de l'institut Fourier

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Let $X$ be a smooth projective surface, $K$ the canonical divisor, $H$ a very ample divisor and $M_{H} (c_{1}, c_{2})$ the moduli space of rank-two vector bundles, $H$ -stable with Chern classes $c_{1}$ and $c_{2}$ . We prove that, if there exists $c_{1}^{'}$ such that $c_{1}$ is numerically equivalent to $2 c_{1}^{'}$ and if $c_{2} - \frac{1}{4} c_{1}^{2}$ is even, greater or equal to $H^{2} + H K + 4$ , then there is no Poincaré bundle on $M_{H} (c_{1}, c_{2}) \times X$ . Conversely, if there exists $c_{1}^{'}$ such that the number $c_{1}^{'} \cdot c_{1}$ is odd or if $\frac{1}{2} c_{1}^{2} - \frac{1}{2} c_{1} \cdot K - c_{2}$ is odd, then there exists a Poincaré bundle on $M_{H} (c_{1}, c_{2}) \times X$ .

Ample vector bundles

Robin Hartshorne (1966)

Publications Mathématiques de l'IHÉS

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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

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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...

Displaying similar documents to “A class of non-algebraic threefolds”

On the cohomological strata of families of vector bundles on algebraic surfaces

Holomorphic rank-2 vector bundles on non-Kähler elliptic surfaces

Poincaré bundles for projective surfaces

Ample vector bundles

Seshadri positive curves in a smooth projective 3 -fold

Seshadri positive curves in a smooth projective $3$ -fold