Mixed Łojasiewicz exponents and \(\log\) canonical thresholds of ideals
Let \({\mathcal O}_n\) be the ring of holomorphic germs \(f:({\mathbb{C}}^n,0)\to \mathbb{C}\). Given a monomial ideal \(I\) of finite colength in \({\mathcal O}_n\), one of the goals of the article is to provide a description, in terms of the Newton polyhedron of \(I\), of the family of Łojasiewicz exponents of \(I\) introduced in [the first author, Math. Z. 262, No. 2, 389--409 (2009; Zbl 1168.32022)]. Some inequalities relating Łojasiewicz exponents and mixed multiplicities are also obtained. Given an ideal \(I\) of finite colength, the authors also study the relation between the sequence of log canonical thresholds of the restrictions of \(I\) to linear subspaces of different dimensions with Łojasiewicz exponents and they obtain an expression for this sequence in terms of Newton polyhedra when the ideal \(I\) is monomial.
scientific article; zbMATH DE number 6499132
scientific article