Grobner bases and extension of scalars

Details Grobner bases and extension of scalars Grobner bases and extension of scalars

1992-02-20

arxiv.org/abs/alg-geom/9202021v1

Mathematics

Algebraic Geometry

18 pages, LaTeX

Scientific paper

This paper studies the behavior of Grobner bases with respect to extensions of scalars. We prove that an extension of scalars commutes with taking Grobner bases iff the extension is flat. We consider what information can be deduced about fibers of a family, from the Grobner basis of the defining ideal of the family itself. This information can be used to construct algorithms, such as to find locii over which a map is finite, or an isomorphism.

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