Exponents of an Irreducible Plane Curve Singularity
نویسندگان
چکیده
exp(2 i( p 1 i ) are the eigenvalues of the Milnor monodromy and their integral part is determined by the Hodge ltration of the mixed Hodge structure. This notion was rst introduced by Steenbrink [11]. By [14] the exponents are constant under -constant deformation of f . In particular, they depend only on f 1 (0). They express the vanishing order (up to the shift by one) of the period integrals of holomorphic forms on vanishing cycles by [12], [13].
منابع مشابه
Poincaré series and zeta function for an irreducible plane curve singularity
The Poincaré series of an irreducible plane curve singularity equals the ζ-function of its monodromy, by a result of Campillo, Delgado and GuseinZade. We derive this fact from a formula of Ebeling and Gusein-Zade relating the Poincaré series of a quasi-homogeneous complete intersection singularity to the Saito dual of a product of ζ-functions. Several cases are known where the ζ-function of the...
متن کاملParametrization of approximate algebraic curves by lines
It is well known that irreducible algebraic plane curves having a singularity of maximum multiplicity are rational and can be parametrized by lines. In this paper, given a tolerance ¿ 0 and an -irreducible algebraic plane curve C of degree d having an -singularity of multiplicity d−1, we provide an algorithm that computes a proper parametrization of a rational curve that is exactly parametrizab...
متن کاملResolving Singularities of Plane Analytic Branches with One Toric Morphism
Let (C; 0) be an irreducible germ of complex plane curve. Let ? N be the semigroup associated to it and C ? C g+1 the corresponding monomial curve, where g is the number of Puiseux exponents of (C; 0). We show, using the specialization of (C;0) to (C ? ; 0), that the same toric morphisms
متن کاملPoincaré series and monodromy of a two-dimensional quasihomogeneous hypersurface singularity
A relation is proved between the Poincaré series of the coordinate algebra of a two-dimensional quasihomogeneous isolated hypersurface singularity and the characteristic polynomial of its monodromy operator. For a Kleinian singularity not of type A2n, this amounts to the statement that the Poincaré series is the quotient of the characteristic polynomial of the Coxeter element by the characteris...
متن کاملConnections on Modules over Quasi-homogeneous Plane Curves
Let k be an algebraically closed field of characteristic 0, and let A = k[x, y]/(f) be a quasi-homogeneous plane curve. We show that for any graded torsion free A-module M without free summands, there exists a natural graded integrable connection, i.e. a graded A-linear homomorphism ∇ : Derk(A) → Endk(M) that satisfy the derivation property and preserves the Lie product. In particular, a torsio...
متن کامل