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Asymptotic cohomology vanishing and a converse to the Andreotti-Grauert theorem on surfaces

Shin-ichi Matsumura (2013)

Annales de l’institut Fourier

In this paper, we study relations between positivity of the curvature and the asymptotic behavior of the higher cohomology group for tensor powers of a holomorphic line bundle. The Andreotti-Grauert vanishing theorem asserts that partial positivity of the curvature implies asymptotic vanishing of certain higher cohomology groups. We investigate the converse implication of this theorem under various situations. For example, we consider the case where a line bundle is semi-ample or big. Moreover,...

Asymptotic invariants of base loci

Lawrence Ein, Robert Lazarsfeld, Mircea Mustaţă, Michael Nakamaye, Mihnea Popa (2006)

Annales de l’institut Fourier

The purpose of this paper is to define and study systematically some asymptotic invariants associated to base loci of line bundles on smooth projective varieties. The functional behavior of these invariants is related to the set-theoretic behavior of base loci.

Bornes pour la régularité de Castelnuovo-Mumford des schémas non lisses

Amadou Lamine Fall (2009)

Annales de l’institut Fourier

Nous montrons dans cet article des bornes pour la régularité de Castelnuovo-Mumford d’un schéma admettant des singularités, en fonction des degrés des équations définissant le schéma, de sa dimension et de la dimension de son lieu singulier. Dans le cas où les singularités sont isolées, nous améliorons la borne fournie par Chardin et Ulrich et dans le cas général, nous établissons une borne doublement exponentielle en la dimension du lieu singulier.

Effective nonvanishing, effective global generation

Mark Andrea A. De Cataldo (1998)

Annales de l'institut Fourier

We prove a multiple-points higher-jets nonvanishing theorem by the use of local Seshadri constants. Applications are given to effectivity problems such as constructing rational and birational maps into Grassmannians, and the global generation of vector bundles.

Geometric genera for ample vector bundles with regular sections.

Antonio Lanteri (2000)

Revista Matemática Complutense

Let X be a smooth complex projective variety of dimension n ≥ 3. A notion of geometric genus pg(X,E) for ample vector bundles E of rank r < n on X admitting some regular sections is introduced. The following inequality holds: pg(X,E) ≥ hn-r,0(X). The question of characterizing equality is discussed and the answer is given for E decomposable of corank 2. Some conjectures suggested by the result are formulated.

Moduli of certain Fano 4-folds.

Walter L. Baily Jr. (2001)

Revista Matemática Iberoamericana

In this brief note we give a proof that a certain family of Fano 4-folds, described below, is complex (locally) complete and effectively parametrized in the sense of Kodaira-Spencer [Ko-Sp].

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