On the Newton filtration for functions on complete intersections

TL;DR

This paper extends the concept of Newton filtrations from hypersurface singularities to complete intersections, aiming to compare with classical filtrations related to Milnor numbers.

Contribution

It introduces a Newton filtration framework for complete intersections, expanding the scope beyond hypersurfaces and enabling new comparisons with classical invariants.

Findings

Developed a generalized Newton filtration for complete intersections

Established connections with classical Newton filtrations and Milnor numbers

Provided insights into the structure of singularities through this new filtration

Abstract

W.Ebeling and S.M.Gusein-Zade have started to look at multi-index Newton filtrations for hypersurface singularities. In this paper we pass to complete intersections. One motivation is the possibility to compare with the "classical" Newton filtration introduced by A.G.Kushnirenko in connection with the Milnor number.