Deterministic Genericity for Polynomial Ideals
Symbolic Computation
2017-05-09 v1 Commutative Algebra
Algebraic Geometry
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.
Cite
@article{arxiv.1705.02797,
title = {Deterministic Genericity for Polynomial Ideals},
author = {Amir Hashemi and Michael Schweinfurter and Werner M. Seiler},
journal= {arXiv preprint arXiv:1705.02797},
year = {2017}
}
Comments
42 pages, to be published in Journal of Symbolic Computation, 2017