Arakelov-Nevanlinna inequalities for variations of Hodge structures and applications
| hal.structure.identifier | Institut Élie Cartan de Lorraine [IECL] | |
| dc.contributor.author | BROTBEK, Damian | |
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | BRUNEBARBE, Yohan | |
| dc.date.accessioned | 2024-04-04T02:48:20Z | |
| dc.date.available | 2024-04-04T02:48:20Z | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/191729 | |
| dc.description.abstractEn | We prove a Second Main Theorem type inequality for any log-smooth projective pair $(X,D)$ such that $X\setminus D$ supports a complex polarized variation of Hodge structures. This can be viewed as a Nevanlinna theoretic analogue of the Arakelov inequalities for variations of Hodge structures due to Deligne, Peters and Jost-Zuo. As an application, we obtain in this context a criterion of hyperbolicity that we use to derive a vast generalization of a well-known hyperbolicity result of Nadel. The first ingredient of our proof is a Second Main Theorem type inequality for any log-smooth projective pair $(X,D)$ such that $X\setminus D$ supports a metric whose holomorphic sectional curvature is bounded from above by a negative constant. The second ingredient of our proof is an explicit bound on the holomorphic sectional curvature of the Griffiths-Schmid metric constructed from a variation of Hodge structures. As a byproduct of our approach, we also establish a Second Main Theorem type inequality for pairs $(X,D)$ such that $X\setminus D$ is hyperbolically embedded in $X$. | |
| dc.language.iso | en | |
| dc.title.en | Arakelov-Nevanlinna inequalities for variations of Hodge structures and applications | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Géométrie algébrique [math.AG] | |
| dc.subject.hal | Mathématiques [math]/Variables complexes [math.CV] | |
| dc.identifier.arxiv | 2007.12957 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-03064645 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-03064645v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=BROTBEK,%20Damian&BRUNEBARBE,%20Yohan&rft.genre=preprint |
Fichier(s) constituant ce document
| Fichiers | Taille | Format | Vue |
|---|---|---|---|
|
Il n'y a pas de fichiers associés à ce document. |
|||