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Quartic double solids with icosahedral symmetry
European Journal of Mathematics. 2016. Vol. 2. No. 1. P. 96-119.
We study quartic double solids admitting icosahedral symmetry.
Prokhorov Y., Sbornik Mathematics 2016 Vol. 207 No. 7 P. 983-1009
We study singular Fano threefolds of type $ V_{22}$. ...
Added: September 3, 2016
Galkin S., / Cornell University. Series math "arxiv.org". 2018. No. 1809.02705.
We classify smooth Fano threefolds that admit degenerations to toric Fano threefolds with ordinary double points. ...
Added: September 25, 2018
Coates T., Corti A., Galkin S. et al., Geometry and Topology 2016 Vol. 20 No. 1 P. 103-256
The quantum period of a variety X is a generating function for certain Gromov-Witten invariants of X which plays an important role in mirror symmetry. In this paper we compute the quantum periods of all 3-dimensional Fano manifolds. In particular we show that 3-dimensional Fano manifolds with very ample anticanonical bundle have mirrors given by ...
Added: November 18, 2014
Cheltsov I., Przyjalkowski V., Shramov K., International Mathematics Research Notices 2019 Vol. 2019 No. 12 P. 3683-3703
We study two rational Fano threefolds with an action of the icosahedral group 𝔄5. The first one is the famous Burkhardt quartic threefold, and the second one is the double cover of the projective space branched in the Barth sextic surface. We prove that both of them are 𝔄5-Fano varieties that are 𝔄5-birationally superrigid. This ...
Added: October 11, 2017
Kuznetsov A., Central European Journal of Mathematics 2012 Vol. 10 No. 4 P. 1198-1231
We introduce the notion of an instanton bundle on a Fano threefold of index 2. For such bundles we give an analogue of a monadic description and discuss the curve of jumping lines. The cases of threefolds of degree 5 and 4 are considered in a greater detail. ...
Added: September 10, 2012
Galkin S., / Cornell University. Series math "arxiv.org". 2018. No. 1809.02738.
We show that G-Fano threefolds are mirror-modular.
1. Mirror maps are inversed reversed Hauptmoduln for moonshine subgroups of SL2(ℝ).
2. Quantum periods, shifted by an integer constant (eigenvalue of quantum operator on primitive cohomology) are expansions of weight 2 modular forms (theta-functions) in terms of inversed Hauptmoduln.
3. Products of inversed Hauptmoduln with some fractional powers of shifted ...
Added: September 25, 2018
Kuznetsov A., Prokhorov Y., Shramov K., / Cornell University. Series arXiv "math". 2016.
We discuss various results on Hilbert schemes of lines and conics and automorphism groups of smooth Fano threefolds with Picard rank 1. Besides a general review of facts well known to experts, the paper contains some new results, for instance, we give a description of the Hilbert scheme of conics on any smooth Fano threefold ...
Added: May 16, 2016
Cheltsov I., Shramov K., CRC Press, 2015
Cremona Groups and the Icosahedron focuses on the Cremona groups of ranks 2 and 3 and describes the beautiful appearances of the icosahedral group A5 in them. The book surveys known facts about surfaces with an action of A5, explores A5-equivariant geometry of the quintic del Pezzo threefold V5, and gives a proof of its A5-birational rigidity.
The authors ...
Added: October 6, 2015
Cheltsov I., Park J., Ahmadinezhad H., / Cornell University. Series arXiv "math". 2020.
We prove that a quasi-smooth Fano threefold hypersurface is birationally rigid if and only if it has Fano index one. ...
Added: August 19, 2020
Cheltsov I., Shramov K., / Cornell University. Series math "arxiv.org". 2018.
We study the problem of existence of K\"ahler--Einstein metrics on smooth Fano threefolds of Picard rank one and anticanonical degree 22 that admit a faithful action of the multiplicative group ℂ∗. We prove that, except possibly two explicitly described cases, all such smooth Fano threefolds are K\"ahler--Einstein. ...
Added: October 21, 2018
Prokhorov Y., Kuznetsov A., Shramov K., Japanese Journal of Mathematics 2018 Vol. 13 No. 1 P. 109-185
We discuss various results on Hilbert schemes of lines and conics and automorphism groups of smooth Fano threefolds of Picard rank 1. Besides a general review of facts well known to experts, the paper contains some new results, for instance, we give a description of the Hilbert scheme of conics on any smooth Fano threefold ...
Added: November 22, 2017
Prokhorov Y., Kuznetsov A., / Cornell University. Series arXiv "math". 2017.
We give an explicit construction of prime Fano threefolds of genus 12 with a G_m-action, describe their isomorphism classes and automorphism groups. ...
Added: November 29, 2017
191574970, Functional Analysis and Its Applications 2006 Vol. 40 No. 2 P. 81-90
It is well known that every module M over the algebra ℒ(X) of operators on a finite-dimensional space X can be represented as the tensor product of X by some vector space E, M ≅ = E ⊗ X. We generalize this assertion to the case of topological modules by proving that if X is a stereotype space with the stereotype approximation property, then for each stereotype module M over the ...
Added: September 23, 2016
Losev A. S., Slizovskiy S., JETP Letters 2010 Vol. 91 P. 620-624
Added: February 27, 2013
Ilyashenko Y., Яковенко С. Ю., М. : МЦНМО, 2013
Предлагаемая книга—первый том двухтомной монографии, посвящённой аналитической теории дифференциальных уравнений.
В первой части этого тома излагается формальная и аналитическая теория нормальных форм и теорема о разрешении особенностей для векторных полей на плоскости.
Вторая часть посвящена алгебраически разрешимым локальным задачам теории аналитических дифференциальных уравнений , квадратичным векторным полям и проблеме локальной классификации ростков векторных полей в комплексной области ...
Added: February 5, 2014
Kalyagin V.A., Koldanov A.P., Koldanov P.A. et al., Physica A: Statistical Mechanics and its Applications 2014 Vol. 413 No. 1 P. 59-70
A general approach to measure statistical uncertainty of different filtration techniques for market network analysis is proposed. Two measures of statistical uncertainty are introduced and discussed. One is based on conditional risk for multiple decision statistical procedures and another one is based on average fraction of errors. It is shown that for some important cases ...
Added: July 19, 2014
Maslov V., Теоретическая и математическая физика 2019 Т. 201 № 1 С. 65-83
We study the process of a nucleon separating from an atomic nucleus from the mathematical standpoint
using experimental values of the binding energy for the nucleus of the given substance. A nucleon becomes
a boson at the instant of separating from a fermionic nucleus. We study the further transformations of
boson and fermion states of separation in a ...
Added: November 1, 2019
Pahomov F., Известия РАН. Серия математическая 2016 Т. 80 № 6 С. 173-216
Полимодальная логика доказуемости
GLP была введена Г. К. Джапаридзе в 1986 г. Она является логикой доказуемости для ряда цепочек предикатов доказуемости возрастающей силы. Всякой полимодальной логике соответствует многообразие полимодальных алгебр. Л. Д. Беклемишевым и А. Виссером был поставлен вопрос о разрешимости элементарной теории свободной GLP-алгебры, порожденной константами 0, 1 [1]. В этой статье для любого натурального n решается аналогичный вопрос для логик GLPn, являющихся ...
Added: December 4, 2017
Sinelshchikov D., Кудряшов Н. А., Theoretical and Mathematical Physics 2018 Vol. 196 No. 2 P. 1230-1240
We study a family of nonautonomous generalized Liénard-type equations. We consider the equivalence problem via the generalized Sundman transformations between this family of equations and type-I Painlevé–Gambier equations. As a result, we find four criteria of equivalence, which give four integrable families of Liénard-type equations. We demonstrate that these criteria can be used to construct ...
Added: February 9, 2019
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
Kolokolov I., Lebedev V., Sizov G. A., Journal of Experimental and Theoretical Physics 2011 Vol. 140 No. 2 P. 387-400
We analyze magnetic kinematic dynamo in a conducting fluid where the stationary shear flow is accompanied by relatively weak random velocity fluctuations. The diffusionless and diffusion regimes are described. The growth rates of the magnetic field moments are related to the statistical characteristics of the flow describing divergence of the Lagrangian trajectories. The magnetic field ...
Added: February 2, 2017
ООО Фирма "Элист", 2014
В книге представлены тезисы докладов I тура XV Всероссийской научно-технической конференции и школы молодых ученых, аспирантов и студентов. ...
Added: October 17, 2014
Min Namkung, Younghun K., Scientific Reports 2018 Vol. 8 No. 1 P. 16915-1-16915-18
Sequential state discrimination is a strategy for quantum state discrimination of a sender’s quantum
states when N receivers are separately located. In this report, we propose optical designs that can
perform sequential state discrimination of two coherent states. For this purpose, we consider not
only binary phase-shifting-key (BPSK) signals but also general coherent states, with arbitrary prior
probabilities. Since ...
Added: November 16, 2020
Vyalyi M., Дискретная математика 1991 Т. 3 № 3 С. 35-45
Added: October 17, 2014