The holomorphy conjecture for ideals in dimension two

Ann Lemahieu (1) , Lise van Proeyen (2)

1 UNS - Université Nice Sophia Antipolis (1965 - 2019)
2 KU Leuven - Catholic University of Leuven = Katholieke Universiteit Leuven

The holomorphy conjecture predicts that the topo-logical zeta function associated to a polynomial f ∈ C[x 1 ,. .. , x n ] and an integer d > 0 is holomorphic unless d divides the order of an eigenvalue of local monodromy of f. In this note, we generalise the holomorphy conjecture to the setting of arbitrary ideals in C[x 1 ,. .. , x n ], and we prove it when n = 2.

Domaines: Mathématiques [math]

Ann Lemahieu, Lise van Proeyen. The holomorphy conjecture for ideals in dimension two. Proceedings of the American Mathematical Society, 2011, 139, pp.3845-3852 ⟨10.1090/S0002-9939-2011-11186-9⟩. ⟨hal-01280034⟩