Entire curves in C-pairs with large irregularity

Autor:	Kebekus, Stefan, Rousseau, Erwan
Rok vydání:	2024
Předmět:	Mathematics - Algebraic Geometry Mathematics - Complex Variables 32C99 32H99 32A22
Druh dokumentu:	Working Paper
Popis:	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 K\"ahler pairs with arbitrary singularities. However, it also strengthens known results for compact K\"ahler 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. Comment: Version 2: Fix cross-references between the papers arXiv:2407.10668, arXiv:2410.01245, and arXiv:2410.00405. Explain the difference between Theorem 1.1 and earlier results
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2410.01245 Zobrazit plný text záznamu View this record from Arxiv