Lionel Darondeau ; Erwan Rousseau - QUASI-POSITIVE ORBIFOLD COTANGENT BUNDLES.

epiga:9841 - Épijournal de Géométrie Algébrique, April 4, 2024, Volume 8 - https://doi.org/10.46298/epiga.2023.9841
QUASI-POSITIVE ORBIFOLD COTANGENT BUNDLES.Article

Authors: Lionel Darondeau ORCID1,2; Erwan Rousseau 3,4

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.


Volume: Volume 8
Published on: April 4, 2024
Accepted on: November 17, 2023
Submitted on: July 27, 2022
Keywords: Ampleness,symmetric differential forms,orbifold cotangent bundles,hyperplane arrangements,Fermat covers,[MATH.MATH-AG]Mathematics [math]/Algebraic Geometry [math.AG],[MATH.MATH-CV]Mathematics [math]/Complex Variables [math.CV]
Funding:
    Source : HAL
  • Feuilletages et géométrie algébrique; Funder: French National Research Agency (ANR); Code: ANR-16-CE40-0008

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