Changements de variable pour un th`eme.

Daniel Barlet (1, 2)

1 IECN - Institut Élie Cartan de Nancy
2 IUF - Institut universitaire de France

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.

Mots clés: change of variable; Vanishing period; Brieskorn module; (a; b)-module; thema; filtered Gauss-Manin system; change of variable.

Domaines: Géométrie algébrique [math.AG]; Variables complexes [math.CV]

Daniel Barlet. Changements de variable pour un th`eme.. 2010. ⟨hal-00466922⟩