Persistent transcendental Bézout theorems

Lev Buhovsky; Iosif Polterovich; Leonid Polterovich; Egor Shelukhin; Vukašin Stojisavljević

doi:10.1017/fms.2024.49

Persistent transcendental Bézout theorems

Lev Buhovsky, Iosif Polterovich, Leonid Polterovich, Egor Shelukhin^*, Vukašin Stojisavljević

^*Corresponding author for this work

School of Mathematical Sciences

University of Montreal

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Article number	e72
Journal	Forum of Mathematics, Sigma
Volume	12
DOIs	https://doi.org/10.1017/fms.2024.49
State	Published - 27 Aug 2024

Keywords

32Axx 55Uxx

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10.1017/fms.2024.49

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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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AU - Shelukhin, Egor

AU - Stojisavljević, Vukašin

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Persistent transcendental Bézout theorems

Abstract

Keywords

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