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$L^{2}$ -estimates and existence theorems for generalized analytic functions in several variables.

Medzhidov, Z.G. (2004)

Sibirskij Matematicheskij Zhurnal

Le problème de Levi dans les fibrés à base de Stein et à fibre une courbe compacte

Jérôme Brun (1977)

Annales de l'institut Fourier

Soit $X$ un fibré holomorphe localement trivial de base une variété de Stein et de fibre une courbe compacte.Si $A$ est un ouvert localement pseudoconvexe de $X$ ne contenant aucune fibre, alors $A$ est de Stein.

Lefschetz fibrations in symplectic geometry.

Donaldson, S.K. (1998)

Documenta Mathematica

Lelong classes on toric manifolds and a theorem of Siciak

Maritza M. Branker, Małgorzata Stawiska (2012)

Annales Polonici Mathematici

We generalize a theorem of Siciak on the polynomial approximation of the Lelong class to the setting of toric manifolds with an ample line bundle. We also characterize Lelong classes by means of a growth condition on toric manifolds with an ample line bundle and construct an example of a nonample line bundle for which Siciak's theorem does not hold.

Levi-Curvature of Manifolds with a Stein Rational Fibration.

H. Azad (1985)

Manuscripta mathematica

Line bundle convexity of pseudoconvex domains in complex manifolds.

Karen R. Pinney (1991)

Mathematische Zeitschrift

Line bundles with partially vanishing cohomology

Burt Totaro (2013)

Journal of the European Mathematical Society

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.