On meromorphic functions defined by a differential system of order 1

Tristan Torrelli (1)

1 IECN - Institut Élie Cartan de Nancy

Given a germ h of holomorphic function on (C^n,0), we study the condition "the ideal Ann_D 1/h is generated by operators of order one." We obtain here full characterizations in the particular cases of Hoszul-free germs and unreduced germ of plane curves. Moreover, we prove that this condition holds for a special type of hypersurface arrangements. These results allow us to link this condition to the comparison of de Rham complexes associated with h.

Mots clés: Germs of meromorphic functions; D-modules; free divisors; arrangements of hyperplanes; logarithmic de Rham complex; logarithmic comparison theorem

Domaines: Géométrie algébrique [math.AG]

Tristan Torrelli. On meromorphic functions defined by a differential system of order 1. Bulletin de la société mathématique de France, 2004, 132 (4), pp.591-612. ⟨hal-00146433⟩