QUASI-POSITIVE ORBIFOLD COTANGENT BUNDLES.

Lionel Darondeau (1) , Erwan Rousseau (2, 3)

1 IMJ-PRG (UMR_7586) - Institut de Mathématiques de Jussieu - Paris Rive Gauche
2 LMBA - Laboratoire de Mathématiques de Bretagne Atlantique
3 UBO - Université de Brest

In this work, we investigate the positivity of logarithmic and orbifold cotangent bundles along hyperplane arrangements in projective spaces. We show that a very interesting example given by Noguchi (as early as in 1986) can be pushed further to a very great extent. Key ingredients of our approach are the use of Fermat covers and the production of explicit global symmetric differentials. This allows us to obtain some new results in the vein of several classical results of the literature on hyperplane arrangements. These seem very natural using the modern point of view of augmented base loci, and working in Campana's orbifold category.

Mots clés: Ampleness; symmetric differential forms; orbifold cotangent bundles; hyperplane arrangements; Fermat covers

Domaines: Géométrie algébrique [math.AG]; Variables complexes [math.CV]

Lionel Darondeau, Erwan Rousseau. QUASI-POSITIVE ORBIFOLD COTANGENT BUNDLES.: PUSHING FURTHER AN EXAMPLE BY JUNJIRO NOGUCHI. Épijournal de Géométrie Algébrique, 2023, 8, ⟨10.46298/epiga.2023.9841⟩. ⟨hal-02896877v4⟩