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Lionel Darondeau ; Erwan Rousseau - Quasi-positive orbifold cotangent bundles
epiga:9841 - Épijournal de Géométrie Algébrique, 4 avril 2024, Volume 8 - https://doi.org/10.46298/epiga.2023.9841Quasi-positive orbifold cotangent bundlesArticle
Auteurs : Lionel Darondeau 
1,2; Erwan Rousseau 3,4
- 1 Institut Montpelliérain Alexander Grothendieck
- 2 Institut de Mathématiques de Jussieu - Paris Rive Gauche
- 3 Laboratoire de Mathématiques de Bretagne Atlantique [UBO]
- 4 Université de Brest [UBO]
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.
Source : HAL:hal-02896877v4
Volume : Volume 8
Publié le : 4 avril 2024
Accepté le : 17 novembre 2023
Soumis le : 27 juillet 2022
Mots-clés : 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]
Financement :
- Source : HAL
- Feuilletages et géométrie algébrique; Financeur: French National Research Agency (ANR); Code: ANR-16-CE40-0008
Classifications
Mathematics Subject Classification 20201
Publications
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