Cohomological characterizations of projective spaces and hyperquadrics

By Carolina Araujo, S. Druel, S'andor J. Kov'acs. 2007

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Projective spaces and hyperquadrics are the simplest projective algebraic varieties, and they can be characterized in many ways. The aim of this paper is to provide a new characterization of them in terms of positivity properties of the tangent bundle (Theorem 1.1). The first result in this direction was Mori’s proof of the Hartshorne conjecture in [Mor79] (see also Siu and Yau [SY80]), that characterizes projective spaces as the only manifolds having ample tangent bundle. Then, in [Wah83], Wahl characterized projective spaces as the only manifolds whose tangent bundles contain ample invertible subsheaves. Interpolating Mori’s and Wahl’s results, Andreatta and Wiśniewski gave the following characterization:

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/f7363327239a673c01d882fb044059821ea94999

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In Geometry and Topology

In Mathematical Physics

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