The discriminant locus of a system of n Laurent polynomials in n variables


Тип публикации: статья из журнала

Год издания: 2012

Идентификатор DOI: 10.1070/IM2012v076n05ABEH002608

Ключевые слова: discriminant locus, linearization of an algebraic system, logarithmic Gauss map

Аннотация: We consider a system of n algebraic equations in n variables, where the exponents of the monomials in each equation are fixed while all the coefficients vary. The discriminant locus of such a system is the closure of the set of all coefficients for which the system has multiple roots with non-zero coordinates. For dehomogenized disПоказать полностьюcriminant loci, we give parametrizations of those irreducible components that depend on the coefficients of all the equations. We prove that if such a component has codimension 1, then the parametrization is inverse to the logarithmic Gauss map of the component (an analogue of Kapranov's result for the A-discriminant). Our argument is based on the linearization of algebraic systems and the parametrization of the set of its critical values.

Ссылки на полный текст



Выпуск журнала: Vol. 76, Is. 5

Номера страниц: 881-906

ISSN журнала: 10645632

Место издания: BRISTOL



  • Antipova I.A. (Institute of Space and Information Technology,Siberian Federal University)
  • Tsikh A.K. (Institute of Mathematics,Siberian Federal University)

Вхождение в базы данных