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

Antipova, I. A.; Tsikh, A. K.

doi:10.1070/im2012v076n05abeh002608

Cited by 10 publications

(14 citation statements)

References 10 publications

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“…Let us show how to calculate the integral (4). A method of the calculation is based on the separating cycle principle formulated in [16] and developed in [17].…”

Section: Mellin-barnes Integral As a Tool Of Analytic Continuationmentioning

confidence: 99%

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Analytic Continuation for Solutions to the System of Trinomial Algebraic Equations

Antipova

Kleshkova

Kulikov

2020

Journal of Siberian Federal University. Mathematics &Amp; Physics

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In the paper, we deal with the problem of getting analytic continuations for the monomial function associated with a solution to the reduced trinomial algebraic system. In particular, we develop the idea of applying the Mellin-Barnes integral representation of the monomial function for solving the extension problem and demonstrate how to achieve the same result following the fact that the solution to the universal trinomial system is polyhomogeneous. As a main result, we construct Puiseux expansions (centred at the origin) representing analytic continuations of the monomial function.

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“…Let us show how to calculate the integral (4). A method of the calculation is based on the separating cycle principle formulated in [16] and developed in [17].…”

Section: Mellin-barnes Integral As a Tool Of Analytic Continuationmentioning

confidence: 99%

“…Proof. Following [4], we carry out the linearization of the system (21). For that we regard (21) as a system of equations in the space C n r × C n y with coordinates r = (r (i) α (i) ), y = (y 1 , .…”

Section: Taylor Series For Monomials Of Solutions To Reduced Systemsmentioning

confidence: 99%

Analytic Continuation for Solutions to the System of Trinomial Algebraic Equations

Antipova

Kleshkova

Kulikov

2020

Journal of Siberian Federal University. Mathematics &Amp; Physics

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“…, y n (a)) of (1) has a polyhomogeneity property, and thus the system usually can be written in a homogenized form by means of monomial transformations x = x(a) of coefficients (see [1]). To do this, it is necessary to distinguish a collection of n exponents ω (i) ∈ A (i) such that the matrix ω = ω (1) , . .…”

Section: Introductionmentioning

confidence: 99%

On facets of the Newton polytope for the discriminant of the polynomial system

Antipova¹,

Kleshkova²

2021

Preprint

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“…where ∆ j = ∂∆ ∂a j are derivatives of the discriminant ∆(a) of the polynomial f (y) in (2). Analogous formulas for a unique root of multiplicity ν 2 are given in [5], where instead of using the discriminant ∆, the resultant of f and its derivative f (ν−1) (with respect to y) of order ν − 1 is used.…”

Section: Introductionmentioning

confidence: 99%

Singular Points of Complex Algebraic Hypersurfaces

Antipova¹,

Mikhalkin²,

Tsikh³

2018

J. Sib. Fed. Univ., Math. phys.

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We consider a complex hypersurface V given by an algebraic equation in k unknowns, where the set A ⊂ Z k of monomial exponents is fixed, and all the coefficients are variable. In other words, we consider a family of hypersurfaces in (C \ 0) k parametrized by its coefficients a = (aα)α∈A ∈ C A. We prove that when A generates the lattice Z k as a group, then over the set of regular points a in the A-discriminantal set, the singular points of V admit a rational expression in a.

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

Cited by 10 publications

References 10 publications

Analytic Continuation for Solutions to the System of Trinomial Algebraic Equations

Analytic Continuation for Solutions to the System of Trinomial Algebraic Equations

On facets of the Newton polytope for the discriminant of the polynomial system

Singular Points of Complex Algebraic Hypersurfaces

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