Characterizations of Projective Spaces and Hyperquadrics via Positivity Properties of the Tangent Bundle

2010/12/09 by Kiana Ross, Ross, Kiana
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Meromorphic and Entire Functions #math.AG

paper · pdf · doi:10.48550/arxiv.1012.2043

Version 2 updates: (1) Added reference to abstract, (2) Updated remark 4.2

arxiv created 2010/12/18 · arxiv updated 2010/12/21

Abstract

Let X be a smooth complex projective variety. A recent conjecture of S. Kovács states that if t he p^th-exterior power of the tangent bundle T_X contains the p^th-exterior power of an ample vector bundle, then X is either a projective space or a smooth quadric hypersurface. This conjecture is appealing since it is a common generalization of Mori's, Wahl's, Andreatt a-Wísniewski's, and Araujo-Druel-Kovács's characterizations of these spaces. In this paper I give a proof affirming this conjecture for varieties with Picard number 1.

Related

• Characterizations of projective spaces and hyperquadrics
• Caractérisations des espaces projectifs et des quadriques
• Characterization theorems for the projective space and vector bundle adjunction
• Positivity of exterior products of tangent bundles and their subsheaves
• Positivity of the exterior power of the tangent bundles