Entire curves in C-pairs with large irregularity

Fuente: arXiv
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Main Authors: Kebekus, Stefan, Rousseau, Erwan
Format: Preprint
Published: 2024
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author Kebekus, Stefan
Rousseau, Erwan
author_facet Kebekus, Stefan
Rousseau, Erwan
contents This paper extends the fundamental theorem of Bloch-Ochiai to the context of C-pairs: If (X, D) is a C-pair with large irregularity, then no entire C-curve in X is ever dense. In its most general form, the paper's main theorem applies to normal Kähler pairs with arbitrary singularities. However, it also strengthens known results for compact Kähler manifolds without boundary, as it applies to some settings that the classic Bloch-Ochiai theorem does not address. The proof builds on the work of Kawamata, Ueno, and Noguchi, recasting parabolic Nevanlinna theory as a "Nevanlinna theory for C-pairs". We hope the approach might be of independent interest.
format Preprint
id arxiv_https___arxiv_org_abs_2410_01245
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Entire curves in C-pairs with large irregularity
Kebekus, Stefan
Rousseau, Erwan
Algebraic Geometry
Complex Variables
32C99, 32H99, 32A22
This paper extends the fundamental theorem of Bloch-Ochiai to the context of C-pairs: If (X, D) is a C-pair with large irregularity, then no entire C-curve in X is ever dense. In its most general form, the paper's main theorem applies to normal Kähler pairs with arbitrary singularities. However, it also strengthens known results for compact Kähler manifolds without boundary, as it applies to some settings that the classic Bloch-Ochiai theorem does not address. The proof builds on the work of Kawamata, Ueno, and Noguchi, recasting parabolic Nevanlinna theory as a "Nevanlinna theory for C-pairs". We hope the approach might be of independent interest.
title Entire curves in C-pairs with large irregularity
topic Algebraic Geometry
Complex Variables
32C99, 32H99, 32A22
url https://arxiv.org/abs/2410.01245