Hyperbolicity Related Problems for Complete Intersection Varieties

Details Hyperbolicity Related Problems for Complete Intersection Varieties Hyperbolicity Related Problems for Complete Intersection Varieties

2011-01-18

arxiv.org/abs/1101.3394v1

Mathematics

Algebraic Geometry

27 pages, no figures, comments are welcome

Scientific paper

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.

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