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arXiv · 2307.02937

Persistent transcendental B\'ezout theorems

Lev Buhovsky·Iosif Polterovich·Leonid Polterovich·Egor Shelukhin·Vukašin Stojisavljević
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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.

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Lev Buhovsky, Iosif Polterovich, Leonid Polterovich, Egor Shelukhin, Vukašin Stojisavljević. 2023-07-06. Persistent transcendental B\'ezout theorems. https://doi.org/10.1017/fms.2024.49

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