Persistent transcendental B\'ezout theorems
Complex Variables
2024-11-20 v3 Algebraic Geometry
Algebraic Topology
Abstract
An example of Cornalba and Shiffman from 1972 disproves in dimension two or higher a classical prediction that the count of zeros of holomorphic self-mappings of the complex linear space should be controlled by the maximum modulus function. We prove that such a bound holds for a modified coarse count inspired by the theory of persistence modules originating in topological data analysis.
Keywords
Cite
@article{arxiv.2307.02937,
title = {Persistent transcendental B\'ezout theorems},
author = {Lev Buhovsky and Iosif Polterovich and Leonid Polterovich and Egor Shelukhin and Vukašin Stojisavljević},
journal= {arXiv preprint arXiv:2307.02937},
year = {2024}
}
Comments
37 pages, 6 figures; revision: simplified proofs, added results about islands