Carles Bivià-Ausina

JACOBIAN IDEALS AND THE NEWTON NON-DEGENERACY CONDITION

In this paper we extract some conclusions about Newton non-degenerate ideals and the computation of Łojasiewicz exponents relative to this kind of ideal. This motivates us to study the Newton non-degeneracy condition on the Jacobian ideal of a given analytic function germ

Newton filtrations, graded algebras and codimension of non-degenerate ideals

f:(mathbb{C}^n,0)to(mathbb{C},0)

The Analytic Spread of Monomial Ideals

. In particular, we establish a connection between Newton non-degenerate functions and functions whose Jacobian ideal is Newton non-degenerate. AMS 2000 Mathematics subject classification: Primary 32S05. Secondary 57R45

Łojasiewicz exponents and resolution of singularities

The computation of dimCOn/I, the codimension of an ideal I in the ring On of holomorphic map germs at the origin in C, is one of the main tools used to calculate geometric invariants of singularities. In general, this calculus is done using the theory of standard basis of the ring On/I. For weighted homogeneous map germs f : (C, 0) → (C, 0) it is known that some geometric invariants are given in terms of its weights and degrees. For instance, Milnor and Orlik gave a formula in [13] for the Milnor number of a weighted homogeneous map germ f : (C, 0) → (C, 0) with an isolated singularity at the origin. There are other invariants that are also computed for weighted homogeneous map germs

Multiplicity and łojasiewicz exponent of generic linear sections of monomial ideals

Abstract We compute the analytic spread of a monomial ideal I of the ring ℂ[[x 1,…,x n ]] in terms of the Newton polyhedron of I.

The Lojasiewicz exponent of a set of weighted homogeneous ideals

We show an effective method to compute the Łojasiewicz exponent of an arbitrary sheaf of ideals of

A Method to Estimate the Degree of

{mathcal{O}_X}

-Sufficiency of Analytic Functions

, where X is a non-singular scheme. This method is based on the algorithm of resolution of singularities.