Analytic continuations of a general algebraic function by means of Puiseux series

Antipova, I. A.; Mikhalkin, E. N.

doi:10.1134/s0081543812080020

Cited by 8 publications

(6 citation statements)

References 11 publications

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“…The convergence domains for the series and integrals representing this function were described in the papers [7] and [8], correspondingly. Using this results, in [9] the monodromy of y(x) was described. We hope that Theorems 2, 3, 4 of this paper can be applied to give a similar description of monodromy for an arbitrary hypergeometric function.…”

Section: Introductionmentioning

confidence: 99%

Domains of Convergence for A-hypergeometric Series and Integrals

Nilsson

Passare

Tsikh

2019

Journal of Siberian Federal University. Mathematics &Amp; Physics

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Section: Introductionmentioning

confidence: 99%

Domains of Convergence for A-hypergeometric Series and Integrals

Nilsson

Passare

Tsikh

2019

Journal of Siberian Federal University. Mathematics &Amp; Physics

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“…равносильных соотношениям (8). Рассмотрим в пространстве CP n−2 с однородными координатами s = (s j ), …”

Section: для краткости письма введем обозначениеunclassified

Singular strata of cuspidal type for the classical discriminant

Mikhalkin¹,

Tsikh²

2015

Математический сборник

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Сингулярные страты каспидального типа для классического дискриминантаРассматривается алгебраическое уравнение с переменными комплекс-ными коэффициентами. Для приведенного дискриминантного множества такого уравнения получены параметризации сингулярных стратов, отве-чающих за наличие корней кратности не меньше j. Эти параметриза-ции являются сужениями параметризации Горна-Капранова всего дискри-минантного множества на цепочку вложенных линейных подпространств проективного пространства. Доказано, что такие страты мономиальными преобразованиями переводятся в приведенные A-дискриминантные мно-жества.Библиография: 12 названий.Ключевые слова: общее алгебраическое уравнение, A-дискриминант-ное множество, параметризация Горна-Капранова, сингулярный страт.

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“…Since every pair consisting of a polydisk domain and a polyhedral domain has nonempty intersection, the solutions expressed as the corresponding series and integrals are analytic continuations of each other. This scheme of analytic continuations is described in [5].…”

Section: Introductionmentioning

confidence: 99%

The monodromy of a general algebraic function

Mikhalkin

2015

Sib Math J

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We consider a general reduced algebraic equation of degree n with complex coefficients. The solution to this equation, a multifunction, is called a general algebraic function. In the coefficient space we consider the discriminant set ∇ of the equation and choose in its complement the maximal polydisk domain D containing the origin. We describe the monodromy of the general algebraic function in a neighborhood of D. In particular, we prove that ∇ intersects the boundary ∂D along n real algebraic surfaces S (j) of dimension n − 2. Furthermore, every branch y j (x) of the general algebraic function ramifies in D only along the pair of surfaces S (j) and S (j−1) .

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Analytic continuations of a general algebraic function by means of Puiseux series

Cited by 8 publications

References 11 publications

Domains of Convergence for A-hypergeometric Series and Integrals

Domains of Convergence for A-hypergeometric Series and Integrals

Singular strata of cuspidal type for the classical discriminant

The monodromy of a general algebraic function

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