Deterministic Genericity for Polynomial Ideals

05/08/2017

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by   Amir Hashemi, et al.

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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.