Yu. Burman, Serge Lvovski, Moscow Mathematical Journal 2015 Vol. 15 No. 1 P. 31-48
Suppose that C ⊂ P^2 is a general enough nodal plane curve
of degree > 2, : \hat C → C is its normalization, and π: C′ → P^1 is a finite
morphism simply ramified over the same set of points as a projection
pr_p ◦ν : \hat C → P1, where p ∈ P^2 ...
Added: January 14, 2015
Gusein-Zade S., Journal of Algebra and its Applications 2018 Vol. 17 No. 10 P. 1-13
In a previous paper, the authors defined an equivariant version of the so-called Saito duality between the monodromy zeta functions as a sort of Fourier transform between the Burnside rings of an abelian group and of its group of characters. Here, a so-called enhanced Burnside ring Bˆ(G) of a finite group G is defined. An ...
Added: October 27, 2020
Vyugin I. V., Успехи математических наук 2011 Т. 66 № 1 (397) С. 37-64
Работа посвящена проблеме Римана–Гильберта для скалярных фуксовых уравнений: задаче построения скалярного фуксова уравнения по представлению монодромии и набору особых точек. Основную часть работы представляют результаты А. А. Болибруха [5], М. Ван-дер-Пута и М. Зингера [7] и автора [10], обобщенные в единую теорему, снабженную новым доказательством. Обсуждаются также некоторые из возможных приложений этих результатов.
Библиография: 16 названий ...
Added: February 27, 2013
Takeuchi K., Esterov A. I., Lemahieu A., / Cornell University. Series math "arxiv.org". 2016. No. arXiv:1309.0630v4.
Recently the second author and Van Proeyen proved the monodromy conjecture on topological zeta functions for all non-degenerate surface singularities. In this paper, we obtain higher-dimensional analogues of their results, which, in particular, prove the conjecture for all isolated singularities of 4 variables, as well as for many classes of non-isolated and higher-dimensional singularities. One ...
Added: September 18, 2017
Serge Lvovski, Moscow Mathematical Journal 2019 Vol. 19 No. 3 P. 597-613
We show that if we are given a smooth non-isotrivial family of curves of genus 1 over C with a smooth base B for which the general fiber of the mapping J : B → A 1 (assigning j-invariant of the fiber to a point) is connected, then the monodromy group of the family (acting ...
Added: August 30, 2019
Esterov A. I., Gusev G. G., Mathematische Annalen 2016 Vol. 365 No. 3 P. 1091-1110
We generalize the Abel–Ruffini theorem to arbitrary dimension, i.e. classify general square systems of polynomial equations solvable by radicals. In most cases, they reduce to systems whose tuples of Newton polytopes have mixed volume not exceeding 4. The proof is based on topological Galois theory, which ensures non-solvability by any formula involving quadratures and single-valued ...
Added: February 27, 2017
Esterov A. I., Takeuchi K., Lemahieu A., Journal of the European Mathematical Society 2021
The monodromy conjecture is an umbrella term for several conjectured relationships between poles of zeta functions, monodromy eigenvalues and roots of Bernstein-Sato polynomials in arithmetic geometry and singularity theory. Even the weakest of these relations --- the Denef--Loeser conjecture on topological zeta functions --- is open for surface singularities. We prove it for a wide ...
Added: November 28, 2020
Vyugin I. V., Гонцов Р. Р., Успехи математических наук 2012 Т. 67 № 3 (405) С. 183-184
Получено обобщение результата Ильяшенко-Хованского, утверждающего, что разрешимость в квадратурах фуксовой системы с малыми коэффициентами эквивалентна ее треугольности. В работе этот результат обобщен на случай систем с малыми собственными значениями матриц вычетов. ...
Added: February 21, 2013
Serge Lvovski, Manuscripta Mathematica 2014 Vol. 145 P. 235-242
We show that using an idea from a paper by Van de Ven one may obtain a
simple proof of Zak's classification of smooth projective surfaces
with zero vanishing cycles. This method of proof allows one to extend
Zak's theorem to the case of finite characteristic. ...
Added: October 14, 2014
Smirnov E., Тутубалина А. А., / Cornell University. Series math "arxiv.org". 2020. No. 2009.14120.
Schubert polynomials for the classical groups were defined by S.Billey and M.Haiman in 1995; they are polynomial representatives of Schubert classes in a full flag variety of a classical group. We provide a combinatorial description for these polynomials, as well as their double versions, by introducing analogues of pipe dreams, or RC-graphs, for the Weyl ...
Added: September 30, 2020
Brav C. I., Thomas H., Compositio Mathematica 2014 Vol. 150 No. 3 P. 343-333
We show that some hypergeometric monodromy groups in Sp(4,Z) split as free or amalgamated products and hence by cohomological considerations give examples of Zariski dense, non-arithmetic monodromy groups of real rank 2. In particular, we show that the monodromy of the natural quotient of the Dwork family of quintic threefolds in P^{4} splits as Z*Z/5. ...
Added: September 29, 2014
Lvovsky S., / Cornell University. Series math "arxiv.org". 2013. No. 1305.2205.
We show that using an idea from a paper by Van de Ven one may obtain a simple proof of Zak's classification of smooth projective surfaces with zero vanishing cycles. This method of proof allows one to extend Zak's theorem to the case of finite characteristic. ...
Added: October 3, 2013
Vyugin I. V., Левин Р. И., Труды Математического института им. В.А. Стеклова РАН 2017 Т. 297 С. 326-343
An analog of the classical Riemann-Hilbert problem formulated for classes of difference and q-difference systems is considered. We propose some strengthening of Birkhoff's existence theorem. ...
Added: August 18, 2017
Burman Y. M., Lvovsky S., / Cornell University. Series math "arxiv.org". 2013. No. 1904.
Suppose that C⊂P2 is a general enough smooth plane curve of degree >2 and that π:C→P1 is a finite morphism simply ramified over the same set of points as a projection prp:C→P1, where p∈P2∖C. We prove that the morphism π is equivalent to such a projection if and only if it extends to a finite ...
Added: November 14, 2013
Esterov A. I., Compositio Mathematica 2019 Vol. 155 No. 2 P. 229-245
We prove that the monodromy group of a reduced irreducible square system of general polynomial equations equals the symmetric group. This is a natural first step towards the Galois theory of general systems of polynomial equations, because arbitrary systems split into reduced irreducible ones upon monomial changes of variables.
In particular, our result proves the multivariate ...
Added: February 5, 2019
Serge Lvovski, / Cornell University. Series arXiv "math". 2017.
We show that the monodromy group acting on $H^1(\cdot,\mathbb Z)$ of a smooth
hyperplane section of a del Pezzo surface over $\mathbb C$ is the entire
group $\mathrm{SL}_2(\mathbb Z)$. For smooth surfaces with $b_1=0$ and hyperplane section
of genus $g>2$, there exist examples in which a similar assertion is
false. Actually, if hyperplane sections of ...
Added: June 14, 2017
V. V. Shevchishin, Izvestiya. Mathematics 2009 Vol. 73 No. 4 P. 797-859
In this paper we prove the non-existence of Lagrangian embeddings of the Klein bottle K in R4 and CP2. We exploit the existence of a special embedding of K in a symplectic Lefschetz pencil pr:X→S2 and study its monodromy. As the main technical tool, we develop the combinatorial theory of mapping class groups. The results ...
Added: March 18, 2013
Esterov A. I., Takeuchi K., Ando K., Advances in Mathematics 2015 Vol. 272 P. 1-19
We study the monodromies at infinity of confluent A-hypergeometric functions introduced by Adolphson. In particular, we compute the monodromy zeta-function. ...
Added: October 10, 2014
Khoroshkin S. M., Tsuboi Z., Journal of Physics A: Mathematical and Theoretical 2014 Vol. 47 P. 1-11
We consider the 'universal monodromy operators' for the Baxter Q-operators. They are given as images of the universal R-matrix in oscillator representation. We find related universal factorization formulas in the Uq(\hat{sl}(2)) case. ...
Added: December 8, 2014
Kudryashov Y., Goncharuk N. B., Bulletin of the Brazilian Mathematical Society 2017 No. 1
In this article we prove in a new way that a generic polynomial vector field in ℂ² possesses countably many homologically independent limit cycles. The new proof needs no estimates on integrals, provides thinner exceptional set for quadratic vector fields, and provides limit cycles that stay in a bounded domain. ...
Added: April 15, 2016
Vladimir L. Popov, Zarhin Y., Indiana University Mathematics Journal 2021 Vol. 70 No. 1 P. 285-300
We classify the types of root systems R in the rings of integers of number fields K such that the Weyl group W(R) lies in the group L(K) generated by Aut(K) and multiplications by the elements of K*. We also classify the Weyl groups of root systems of rank n which are isomorphic to a ...
Added: February 27, 2021
Kotelnikova M. V., Aistov A., Вестник Нижегородского университета им. Н.И. Лобачевского. Серия: Социальные науки 2019 Т. 55 № 3 С. 183-189
The article describes a method that allows to improve the content of disciplines of the mathematical cycle by dividing them into invariant (general) and variable parts. The invariants were identified for such disciplines as «Linear algebra», «Mathematical analysis», «Probability theory and mathematical statistics» delivered to Bachelors program students of economics at several universities. Based on ...
Added: January 28, 2020
Borzykh D., ЛЕНАНД, 2021
Книга представляет собой экспресс-курс по теории вероятностей в контексте начального курса эконометрики. В курсе в максимально доступной форме изложен тот минимум, который необходим для осознанного изучения начального курса эконометрики. Данная книга может не только помочь ликвидировать пробелы в знаниях по теории вероятностей, но и позволить в первом приближении выучить предмет «с нуля». При этом, благодаря доступности изложения и небольшому объему книги, ...
Added: February 20, 2021
В. Л. Попов, Математические заметки 2017 Т. 102 № 1 С. 72-80
Мы доказываем, что аффинно-треугольные подгруппы являются борелевскими подгруппами групп Кремоны. ...
Added: May 3, 2017