Global multiplicity, special closure and non-degeneracy of gradient maps

Bivià-Ausina C.; Huarcaya J.A.C. · Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas (2023) · DOI: 10.1007/s13398-023-01452-4

Resumen

Given a polynomial map F: Cn⟶ Cp with finite zero set, p⩾ n , we introduce the notion of global multiplicity m (F) associated to F, which is analogous to the multiplicity of ideals in Noetherian local rings. This notion allows to characterize numerically the Newton non-degeneracy at infinity of F. This fact motivates us to study a combinatorial inequality concerning the normalized volume of global Newton polyhedra and to characterize the corresponding equality using special closures. We also study the Newton non-degeneracy at infinity of gradient maps.

Instituciones: Universidad Nacional Mayor de San Marcos