Changements de variable pour un th`eme.

Details Changements de variable pour un th`eme. Changements de variable pour un th`eme.

2010-03-26

arxiv.org/abs/1003.5070v1

Mathematics

Algebraic Geometry

Scientific paper

We study the behaviour of the notion of "thema", introduced in our previous article [B.09b], by a change of variable. We show not only that the fundamental invariants of such a thema, corresponding to the Bernstein polynomial, are stable by a change of variable, but also other numerical invariants called principal parameters. \\ We show on a rank 3 example that nevertheless the isomorphism class of a thema is not stable in general by a change of variable. We conclude in proving that a change of variable transforms an holomorphic family of thema in an holomorphic family. This implies that non principal parameters change holomorphically.

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