Algebraic differential equations associated to some polynomials

Daniel Barlet (1)

1 IECL - Institut Élie Cartan de Lorraine

We compute the Gauss-Manin differential equation for any period of a polynomial in \ $\C[x_{0},\dots, x_{n}]$ \ with \ $(n+2)$ \ monomials. We give two general factorizations theorem in the algebra \ $\C< z, (\frac{\partial}{\partial z})^{-1}>$ \ for such a differential equations.

Mots clés: Gauss-Manin connection; Periods; vanishing cycles; Gauss-Manin connection.

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

Daniel Barlet. Algebraic differential equations associated to some polynomials. 2014. ⟨hal-00827514v2⟩