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arXiv · 1705.02797

Deterministic Genericity for Polynomial Ideals

Amir Hashemi·Michael Schweinfurter·Werner M. Seiler
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Abstract

We consider several notions of genericity appearing in algebraic geometry and commutative algebra. Special emphasis is put on various stability notions which are defined in a combinatorial manner and for which a number of equivalent algebraic characterisations are provided. It is shown that in characteristic zero the corresponding generic positions can be obtained with a simple deterministic algorithm. In positive characteristic, only adapted stable positions are reachable except for quasi-stability which is obtainable in any characteristic.

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Amir Hashemi, Michael Schweinfurter, Werner M. Seiler. 2017-05-08. Deterministic Genericity for Polynomial Ideals. https://arxiv.org/abs/1705.02797

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