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Varieties with generically nef tangent bundles

Thomas Peternell (2012)

Journal of the European Mathematical Society

We study various "generic" nefness and ampleness notions for holomorphic vector bundles on a projective manifold. We apply this in particular to the tangent bundle and investigate the relation to the geometry of the manifold.

Zero-dimensional subschemes of ruled varieties

Edoardo Ballico, Cristiano Bocci, Claudio Fontanari (2004)

Open Mathematics

Here we study zero-dimensional subschemes of ruled varieties, mainly Hirzebruch surfaces and rational normal scrolls, by applying the Horace method and the Terracini method

Zeros of bounded holomorphic functions in strictly pseudoconvex domains in 2

Jim Arlebrink (1993)

Annales de l'institut Fourier

Let D be a bounded strictly pseudoconvex domain in 2 and let X be a positive divisor of D with finite area. We prove that there exists a bounded holomorphic function f such that X is the zero set of f . This result has previously been obtained by Berndtsson in the case where D is the unit ball in 2 .

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