Newton non-degenerate polynomial ideals

• Grant number: 11/10653-6
• Support Opportunities: Scholarships in Brazil - Doctorate
• Start date: September 01, 2011
• End date: July 31, 2015
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Marcelo Jose Saia
• Grantee: Jorge Alberto Coripaco Huarcaya
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Associated research grant: 08/54222-6 - Singularities, geometry and differential equations, AP.TEM
• Associated scholarship(s): 12/22365-8 - Nondegenerate ideals in the ring of polynomials, BE.EP.DR

Abstract

Kouchnirenko in 1976 shows a formula to compute the Milnor number of isolated singularity germs of functions in terms of the Newton polyhedron of the germ. Bivia-Ausina, Fukui and Saia in 2002 characerized a class of finite codimension ideals in the ring of formal power series which satisfy a Newton non degeneracy condition, moreover they showed how to compute the Hilbert Samuel multiplicity of such ideals in term of a convenient Newton polyhedron. On the other side Kouchnirenko shows a formula to compute the Milnor number of Newton non degenerate polinomilas in terms of its Newton polyhedron. The main purppose of this project is to develop a study about the Newton non degeneracy condition for ideals in the ring of polinomial functions C[x] and methods to compute the multiplicity in terms of convenient Newton polyhedra. We shall also develope this study to the class of Laurent polynomials, following the ideas of Kouchnirenko.

Academic Publications

(References retrieved automatically from State of São Paulo Research Institutions)

HUARCAYA, Jorge Alberto Coripaco. Non-degeneracy of polynomial maps with respect to global Newton polyhedra. 2015. Doctoral Thesis - Universidade de São Paulo (USP). Instituto de Ciências Matemáticas e de Computação (ICMC/SB) São Carlos.