Desingularization of binomial varieties in arbitrary characteristic. Part I. A new resolution function and their properties | Zendy

Blanco Rocío | Zendy

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Desingularization of binomial varieties in arbitrary characteristic. Part I. A new resolution function and their properties

Author(s) -

Blanco Rocío

Publication year - 2012

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.201100108

Subject(s) - mathematics , binomial (polynomial) , binomial coefficient , resolution (logic) , ideal (ethics) , divisor (algebraic geometry) , binomial theorem , function (biology) , binomial approximation , gaussian binomial coefficient , field (mathematics) , monomial ideal , order (exchange) , subroutine , monomial , pure mathematics , discrete mathematics , negative binomial distribution , mathematical analysis , statistics , polynomial ring , computer science , law , polynomial , finance , artificial intelligence , evolutionary biology , economics , poisson distribution , biology , operating system , political science

In this paper we construct a resolution function that will provide an algorithm of resolution of singularities for binomial ideals, over a field of arbitrary characteristic. For us, a binomial ideal means an ideal generated by binomial equations without any restriction, including monomials and p ‐th powers, where p is the characteristic of the base field. This resolution function is based in a modified order function, called E ‐order. The E ‐order of a binomial ideal is the order of the ideal along a normal crossing divisor E . The resolution function allows us to construct an algorithm of E ‐ resolution of binomial basic objects , that will be a subroutine of the main resolution algorithm.

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