A footnote to a paper by Noma

Antonio Lanteri; Francesco Russo

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Displaying similar documents to “A footnote to a paper by Noma”

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...

Nesting maps of Grassmannians

Corrado De Concini, Zinovy Reichstein (2004)

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

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Let $F$ be a field and $G r (i, F^{n})$ be the Grassmannian of $i$ -dimensional linear subspaces of $F^{n}$ . A map $f : G r (i, F^{n}) \to G r (j, F^{n})$ is called nesting if $l \subset f (l)$ for every $l \in G r (i, F^{n})$ . Glover, Homer and Stong showed that there are no continuous nesting maps $G r (i, C^{n}) \to G r (j, C^{n})$ except for a few obvious ones. We prove a similar result for algebraic nesting maps $G r (i, F^{n}) \to G r (j, F^{n})$ , where $F$ is an algebraically closed field of arbitrary characteristic. For $i = 1$ this yields a description of the algebraic sub-bundles of the tangent bundle to the projective space $P_{F}^{n}$ .

Line bundles with partially vanishing cohomology

Burt Totaro (2013)

Journal of the European Mathematical Society

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Define a line bundle $L$ on a projective variety to be $q$ -ample, for a natural number $q$ , if tensoring with high powers of $L$ kills coherent sheaf cohomology above dimension $q$ . Thus 0-ampleness is the usual notion of ampleness. We show that $q$ -ampleness of a line bundle on a projective variety in characteristic zero is equivalent to the vanishing of an explicit finite list of cohomology groups. It follows that $q$ -ampleness is a Zariski open condition, which is not clear from the definition. ...

Parametrized Borsuk-Ulam problem for projective space bundles

Mahender Singh (2011)

Fundamenta Mathematicae

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Let π: E → B be a fiber bundle with fiber having the mod 2 cohomology algebra of a real or a complex projective space and let π’: E’ → B be a vector bundle such that ℤ₂ acts fiber preserving and freely on E and E’-0, where 0 stands for the zero section of the bundle π’: E’ → B. For a fiber preserving ℤ₂-equivariant map f: E → E’, we estimate the cohomological dimension of the zero set $Z_{f} = x \in E | f (x) = 0$ . As an application, we also estimate the cohomological dimension of the ℤ₂-coincidence set $A_{f} = x \in E | f (x) = f (T (x))$ of a...

C-semigroup bundles and C-algebras whose irreducible representations are all finite dimensional

Thomas Müller

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We investigate the structure of C*-algebras with a finite bound on the dimensions of their irreducible representations, sometimes called “subhomogeneous”.In the first chapter we develop the theory of C*-semigroup bundles. These are C*-bundles over semigroups together with a “structure map” which links the semigroup structure of the base space lo the bundle. Under suitable conditions we prove the existence of “enough” bounded sections, which arc “compatible” with the C*-semigroup bundle...

Vanishing of sections of vector bundles on 0-dimensional schemes

Edoardo Ballico (1999)

Commentationes Mathematicae Universitatis Carolinae

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Here we give conditions and examples for the surjectivity or injectivity of the restriction map $H^{0} (X, F) \to H^{0} (Z, F | Z)$ , where $X$ is a projective variety, $F$ is a vector bundle on $X$ and $Z$ is a “general” $0$ -dimensional subscheme of $X$ , $Z$ union of general “fat points”.

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 $P^{3}$ .

Displaying similar documents to “A footnote to a paper by Noma”

A criterion for virtual global generation

Nesting maps of Grassmannians

Line bundles with partially vanishing cohomology

Parametrized Borsuk-Ulam problem for projective space bundles

C*-semigroup bundles and C*-algebras whose irreducible representations are all finite dimensional

Vanishing of sections of vector bundles on 0-dimensional schemes

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

C-semigroup bundles and C-algebras whose irreducible representations are all finite dimensional