Persistent transcendental Bézout theorems
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arXiv
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| Main Authors: | , , , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866909395167739904 |
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| author | Buhovsky, Lev Polterovich, Iosif Polterovich, Leonid Shelukhin, Egor Stojisavljević, Vukašin |
| author_facet | Buhovsky, Lev Polterovich, Iosif Polterovich, Leonid Shelukhin, Egor Stojisavljević, Vukašin |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_02937 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Persistent transcendental Bézout theorems Buhovsky, Lev Polterovich, Iosif Polterovich, Leonid Shelukhin, Egor Stojisavljević, Vukašin Complex Variables Algebraic Geometry Algebraic Topology 32Axx, 55Uxx 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. |
| title | Persistent transcendental Bézout theorems |
| topic | Complex Variables Algebraic Geometry Algebraic Topology 32Axx, 55Uxx |
| url | https://arxiv.org/abs/2307.02937 |