Nondegenerate ideals in the ring of polynomials

• Grant number: 12/22365-8
• Support Opportunities: Scholarships abroad - Research Internship - Doctorate
• Start date: April 01, 2013
• End date: March 31, 2014
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Geometry and Topology
• Principal Investigator: Marcelo Jose Saia
• Grantee: Jorge Alberto Coripaco Huarcaya
• Supervisor: Carles Bivià-Ausina
• Host Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
• Institution abroad: Universitat Politécnica de Valéncia (UPV), Spain
• Associated to the scholarship: 11/10653-6 - Newton non-degenerate polynomial ideals, BP.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 objective this work is to develop a global study on the case of ideal of finite codimension in the ring of polynomials and generalize the results obtained by Bivià-Ausina, Fukui and Saia in 2002, with the determination of a class of ideals which satisfies a condition of Newton non-degeneracy and methods to the calculation of its multiplicities in terms of volumes of polyhedra Newton convenient. We shall also develope this study to the ideals of finite codimension in the class of Laurent polynomials. (AU)

Scientific publications

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

BIVIA-AUSINA, CARLES; HUARCAYA, JORGE A. C.. The Special Closure of Polynomial Maps and Global Non-degeneracy. Mediterranean Journal of Mathematics, v. 14, n. 2, APR 2017. (12/22365-8)

BIVIA-AUSINA, CARLES; HUARCAYA, JORGE A. C.. Polynomial maps with maximal multiplicity and the special closure. MONATSHEFTE FUR MATHEMATIK, v. 188, n. 3, p. 413-429, MAR 2019. (12/22365-8)

BIVIA-AUSINA, CARLES; HUARCAYA, JORGE A. C.. Growth at infinity and index of polynomial maps. Journal of Mathematical Analysis and Applications, v. 422, n. 2, p. 1414-1433, FEB 15 2015. (12/22365-8)