Weak K\"ahler hyperbolicity is birational
Francesco Bei, Beno\^it Claudon, Simone Diverio, Stefano Trapani
TL;DR
This paper proves that if a compact K"ahler manifold is bimeromorphic to a weakly K"ahler hyperbolic manifold, then it is also weakly K"ahler hyperbolic, addressing a question posed by Kollár in 1995.
Contribution
It establishes the birational invariance of weak K"ahler hyperbolicity for compact K"ahler manifolds, resolving a long-standing open problem.
Findings
Weak K"ahler hyperbolicity is preserved under bimeromorphic maps.
The result confirms the birational invariance of weak K"ahler hyperbolicity.
Provides an answer to Kollár's 1995 problem.
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"
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsGeometry and complex manifolds · Geometric and Algebraic Topology · Algebraic Geometry and Number Theory