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The goal of this paper is to show that there are strong relations between certain Monge-Ampère integrals appearing in holomorphic Morse inequalities, and asymptotic cohomology estimates for tensor powers of holomorphic line bundles. Especially, we prove that these relations hold without restriction for projective surfaces, and in the special case of the volume, i.e. of asymptotic $0$ -cohomology, for all projective manifolds. These results can be seen as a partial converse to the Andreotti-Grauert...

A Criterion for the Canonical Bundle of a 3-Fold to be Amble.

Kenji Matsuki (1986)

Mathematische Annalen

A Criterion for the Splitting of a Vector Bundle.

George R. Kempf (1990)

Forum mathematicum

A criterion for virtual global generation

Indranil Biswas, A. J. Parameswaran (2006)

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze

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 if ${(F_{X}^{m})}^{*} E ≅ E_{a} \oplus E_{f}$ for...

A criterion of openness of a family of nef line bundles.

Atsuhsi Moriwaki (1992)

Manuscripta mathematica

A curve of genus $q$ with a Half-Canonical embedding in $\mathbf{P}^{3}$

Sevin Recillas (1984)

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

Si costruiscono curve di genere $g=4n—3$ , $n\geq 3$ che hanno $2^{n-3}(2^{n-2}-1)$ fasci semicanonici $L$ tali che $h^{0}(L)=4$ . Per $n+3$ si dimostra che gli $L$ sono molto ampi.

A Decomposability Criterion for Algebraic 2-Bundles on Projective Spaces.

W. Barth, A. de Van de Ven (1974)

Inventiones mathematicae

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