Vanishing of sections of vector bundles on 0-dimensional schemes

Edoardo Ballico

Displaying similar documents to “Vanishing of sections of vector bundles on 0-dimensional schemes”

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 $P^{3}$ .

A splitting criterion for rank 2 vector bundles on hypersurfaces in $ℙ^{4}$ .

Madonna, C. (1998)

Rendiconti del Seminario Matematico

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On rank $2$ semistable vector bundles over an irreducible nodal curve of genus $2$

Sonia Brivio (1998)

Bollettino dell'Unione Matematica Italiana

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Sia $C$ una curva irriducibile nodale di genere aritmetico $p_{a} = 2$ . In queste note vogliamo mostrare come il sistema lineare delle quadriche, contenenti un opportuno modello proiettivo della curva, permette di descrivere i fibrati vettoriali semistabili, di rango $2$ , su $C$ .

A criterion for virtual global generation

Indranil Biswas, A. J. Parameswaran (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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Let $X$ be a smooth projective curve defined over an algebraically closed field $k$ , and let $F_{X}$ denote the absolute Frobenius morphism of $X$ when the characteristic of $k$ is positive. A vector bundle over $X$ is called virtually globally generated if its pull back, by some finite morphism to $X$ from some smooth projective curve, is generated by its global sections. We prove the following. If the characteristic of $k$ is positive, a vector bundle $E$ over $X$ is virtually globally generated if and only...

Multiplication of sections of stable vector bundles: the injectivity range.

Ballico, E. (2001)

Rendiconti del Seminario Matematico

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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 $M_{H} (c_{1}, c_{2}) \times X$ .

Displaying similar documents to “Vanishing of sections of vector bundles on 0-dimensional schemes”

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

A splitting criterion for rank 2 vector bundles on hypersurfaces in ℙ 4 .

On rank 2 semistable vector bundles over an irreducible nodal curve of genus 2

A criterion for virtual global generation

Multiplication of sections of stable vector bundles: the injectivity range.

Poincaré bundles for projective surfaces

A splitting criterion for rank 2 vector bundles on hypersurfaces in $ℙ^{4}$ .

On rank $2$ semistable vector bundles over an irreducible nodal curve of genus $2$