Hyperbolicity Related Problems for Complete Intersection Varieties

Abstract

In this paper we examine different problems regarding complete intersection varieties of high degree in a complex projective space. First we show how one can deduce hyperbolicity for generic complete intersection of high multidegree and high codimension from the known results on hypersurfaces. Then we prove a existence theorem for jet differentials that generalizes a theorem of S. Diverio. Finally, motivated by a conjecture of O. Debarre, we focus on the positivity of the cotangent bundle of complete intersections, and prove some results towards this conjecture; among other things, we prove that a generic complete intersection surface of high multidegree in a projective space of dimension at least four has ample cotangent bundle.

27 pages, no figures, comments are welcome

References in corpus (2)

• Effective algebraic degeneracy
• Families of hypersurfaces of large degree

Cited by in corpus (4)

• Symmetric differentials and the fundamental group
• Demailly's notion of algebraic hyperbolicity: geometricity, boundedness, moduli of maps
• Boundedness in families with applications to arithmetic hyperbolicity
• Effective bounds on ampleness of cotangent bundles