The Łojasiewicz exponent of a set of weighted homogeneous ideals

Abstract

We give an expression for the Łojasiewicz exponent of a set of ideals which are pieces of a weighted homogeneous filtration. We also study the application of this formula to the computation of the Łojasiewicz exponent of the gradient of a semi-weighted homogeneous function $(\C^n,0)\to (\C,0)$ with an isolated singularity at the origin.

arXiv comment15 pages

References in corpus (1)

• Lojasiewicz exponents and resolution of singularities

Cited by in corpus (3)

• Lojasiewicz exponent of families of ideals, Rees mixed multiplicities and Newton filtrations
• Resolution of singularities and geometric proofs of the Lojasiewicz inequalities
• The sequence of mixed Łojasiewicz exponents associated to pairs of ideals