Weak K\"ahler hyperbolicity is birational
Algebraic Geometry
2024-10-10 v2 Complex Variables
Abstract
We show that a compact K\"ahler manifold bimeromorphic to a weakly K\"ahler hyperbolic manifold is weakly K\"ahler hyperbolic, providing an answer to a problem raised by J. Koll\'ar in his 1995 book "Shafarevic maps and automorphic forms"
Cite
@article{arxiv.2406.01734,
title = {Weak K\"ahler hyperbolicity is birational},
author = {Francesco Bei and Benoît Claudon and Simone Diverio and Stefano Trapani},
journal= {arXiv preprint arXiv:2406.01734},
year = {2024}
}
Comments
16 pages, no figures, comments are very welcome! v2: fixed some typos (including in the title), Corollary 1.3 and Theorem 5.1 are improved, and Corollary 1.4 is new