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Paper   IPM / M / 15051
School of Mathematics
  Title:   Deterministic genericity for polynomial ideals
  Author(s):  Amir Hashemi (Joint with M. Schweinfurter and W. M. Seiler)
  Status:   Published
  Journal: Journal of Symbolic Computation
  Vol.:  86
  Year:  2018
  Pages:   20-50
  Supported by:  IPM
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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