Ampleness of Schur powers of cotangent bundles and k-hyperbolicity
Algebraic Geometry
2021-01-11 v2 Complex Variables
Abstract
In this paper, we study a variation of a conjecture of Debarre on positivity of cotangent bundles of complete intersections. We establish the ampleness of Schur powers of cotangent bundles of generic complete intersections in projective manifolds, with high enough explicit codimension and multi-degrees. Our approach is naturally formulated in terms of flag bundles and allows one to reach the optimal codimension. On complex manifolds, this ampleness property implies intermediate hyperbolic properties. We give a natural application of our main result in this context.
Keywords
Cite
@article{arxiv.1907.09174,
title = {Ampleness of Schur powers of cotangent bundles and k-hyperbolicity},
author = {Antoine Etesse},
journal= {arXiv preprint arXiv:1907.09174},
year = {2021}
}