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Ampleness of Schur powers of cotangent bundles and k-hyperbolicity

Ampleness of Schur powers of cotangent bundles and k-hyperbolicity In this paper, we study a variation in 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. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Research in the Mathematical Sciences Springer Journals

Ampleness of Schur powers of cotangent bundles and k-hyperbolicity

Etesse, Antoine
Research in the Mathematical Sciences , Volume 8 (1) – Jan 25, 2021
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22 pages

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Publisher
Springer Journals
Copyright
Copyright © The Author(s), under exclusive licence to Springer Nature Switzerland AG part of Springer Nature 2021
eISSN
2197-9847
DOI
10.1007/s40687-020-00243-2
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Abstract

In this paper, we study a variation in 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.

Journal

Research in the Mathematical Sciences – Springer Journals

Published: Jan 25, 2021

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