Some Remarks on Generic Complete Intersection Varieties

TL;DR

This paper establishes new existence results for jet differentials on complete intersection varieties, leading to hyperbolicity conclusions for high-degree cases and addressing a conjecture of Debarre with numerical insights.

Contribution

It generalizes Diverio's theorem on jet differentials, connects hyperbolicity to multidegree conditions, and proves a numerical aspect of Debarre's conjecture.

Findings

Existence of jet differentials on complete intersection varieties.

Hyperbolicity for generic complete intersections of high multidegree.

Numerical validation of Debarre's conjecture.

Abstract

We prove an existence theorem for jet differentials on complete intersection varieties that generalizes a theorem of S. Diverio. We also show that one can readily deduce hyperbolicity for generic complete intersections of high multidegree from earlier work of Diverio-Merker-Rousseau and Diverio-Trapani. And finally we prove the numerical aspect of a conjecture of O. Debarre.