test_moissonnage_selune
type: Agent

Projective varieties with ample cotangent bundle
type: Dataset
contact point: Organization
  fn: CCSD
keyword: inegalites-de-morse-holomorphes
keyword: conjecture-de-debarre
keyword: formes-differentielles-symetriques
keyword: varietes-intersection-complete
keyword: equations-differentielles-de-jets
keyword: mathmath-agmathematics-mathalgebraic-geometry-mathag
keyword: positivite-du-fibre-cotangent
keyword: hyperbolicite-au-sens-de-kobayashi
keyword: theoremes-dannulation
keyword: theses
keyword: infoeu-reposemanticsdoctoralthesis
landing page: https://theses.hal.science/tel-00677065
description: We study different hyperbolicity related problems for complete intersection varieties. Given a smooth complete intersection variety X ⊂ M in a smooth complex projective variety M, we prove that if k is bigger than dimX/codimM X and if the multidegree of X is sufficiently big then there exists invariant jet differential equations on X of order k and degree m for m big enough. Then we study a conjecture of O. Debarre: if X ⊂ P^N is the intersection of at least N/2 generic hypersurfaces of sufficiently high degree, then the cotangent bundle of X is ample. We give different results towards this conjecture. We prove that if X satisfies the hypothesis of the conjecture, then X is hyperbolic and the cotangent bundle of X is numerically positive, big, and ample modulo a subset of codimension at least 2. We also give a strategy to compute explicitly symmetric differential forms on particular complete intersection varieties. Then, we prove a vanishing theorem for the cohomology of the Green-Griffiths jet differential bundles, generalizing a result of Schneider and a result of Diverio. Finally, we study the cohomology of line bundles on the universal hypersurface of divisors in P^1.
issued: 2026-05-25T12:46:12.811842
language: en
modified: 2026-05-25T12:46:12.811859

Projective varieties with ample cotangent bundle
type: Distribution
access URL: https://theses.hal.science/tel-00677065
format: HTML
issued: 2026-05-25T12:46:12.834785
modified: 2026-05-25T12:46:12.761003