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AbstractAbstract
[en] We prove that any two irreducible cuspidal Hurwitz curves C0 adn C1 (or, more generally, two curves with A-type singularities) in the Hirzebruch surface FN with the same homology classes and sets of singularities are regular homotopic. Moreover, they are symplectically regular homotopic if C0 and C1 are symplectic with respect to a compatible symplectic form
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Source
Available from http://dx.doi.org/10.1070/IM2004v068n03ABEH000487; Country of input: International Atomic Energy Agency (IAEA)
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Journal Article
Journal
Izvestiya. Mathematics; ISSN 1064-5632;
; v. 68(3); p. 521-542

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Ivanov, A. N.; Tikhomirov, A. S., E-mail: anivanov_1@edu.hse.ru2017
AbstractAbstract
[en] A new irreducible component of the Gieseker–Maruyama moduli scheme M(3) of semistable coherent sheaves of rank 2 with Chern classes c1 = 0, c2 = 3, and c3 = 0 on P3 such that its general point corresponds to a sheaf whose singular locus contains components of dimensions 0 and 1 is described. These sheaves are obtained by elementary transformations of stable reflexive sheaves of rank 2 with Chern classes c1 = 0, c2 = 2, and c3 = 2 along the projective line. The constructed family of sheaves is the first example of an irreducible component of a Gieseker–Maruyama scheme whose general point corresponds to a sheaf with singularities of mixed dimension.
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Source
Copyright (c) 2017 Pleiades Publishing, Ltd.; Country of input: International Atomic Energy Agency (IAEA)
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Journal Article
Journal
Doklady Mathematics (Online); ISSN 1531-8362;
; v. 96(2); p. 506-509

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Bedford, Eric; Kim, Kyounghee; Tuyen Trung Truong; Abarenkova, Nina; Maillard, Jean-Marie, E-mail: bedford@indiana.edu, E-mail: kim@math.fsu.edu, E-mail: truongt@indiana.edu, E-mail: nina@pdmi.ras.ru, E-mail: maillard@lptmc.jussieu.fr2008
AbstractAbstract
[en] We compute the degree complexity of a family of birational mappings of the plane with high order singularities
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Source
Copyright (c) 2008 Springer Science+Business Media B.V.; Country of input: International Atomic Energy Agency (IAEA)
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Journal Article
Journal
Mathematical Physics, Analysis and Geometry; ISSN 1385-0172;
; v. 11(1); p. 53-71

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AbstractAbstract
No abstract available
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Source
Available from http://dx.doi.org/10.1070/PU2008v051n06ABEH006550; Abstract only; Country of input: International Atomic Energy Agency (IAEA)
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Journal Article
Journal
Physics Uspekhi; ISSN 1063-7869;
; v. 51(6); p. 609-616

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Fewster, Christopher J; Kontou, Eleni-Alexandra, E-mail: chris.fewster@york.ac.uk, E-mail: eleni.kontou@york.ac.uk2020
AbstractAbstract
[en] The original singularity theorems of Penrose and Hawking were proved for matter obeying the null energy condition or strong energy condition, respectively. Various authors have proved versions of these results under weakened hypotheses, by considering the Riccati inequality obtained from Raychaudhuri’s equation. Here, we give a different derivation that avoids the Raychaudhuri equation but instead makes use of index form methods. We show how our results improve over existing methods and how they can be applied to hypotheses inspired by quantum energy inequalities. In this last case, we make quantitative estimates of the initial conditions required for our singularity theorems to apply. (paper)
Primary Subject
Source
Available from http://dx.doi.org/10.1088/1361-6382/ab685b; Country of input: International Atomic Energy Agency (IAEA)
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Journal Article
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AbstractAbstract
[en] We study the behaviour as /x/ → 0 of the solutions u=u(x) of the equation (1) Δu=V(/x/)u defined for 0
[fr]
On etudie le comportement en 0 des solutions u=u(x) de l'equation (1) Δu=V(/x/)u definies pour 0
Original Title
Singularites isolees et comportement a l'infini des solutions de l'equation de Schroedinger stationnaire
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Journal Article
Journal
Comptes Rendus des Seances de l'Academie des Sciences. Serie 1; v. 300(4); p. 105-108
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AbstractAbstract
No abstract available
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Source
Available from http://dx.doi.org/10.1070/RM2010v065n05ABEH004709; Abstract only; Country of input: International Atomic Energy Agency (IAEA)
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Journal Article
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Prokofev, V; Zabrodin, A, E-mail: vadim.prokofev@phystech.edu, E-mail: zabrodin@itep.ru2021
AbstractAbstract
[en] We consider solutions of the Kadomtsev–Petviashvili hierarchy which are elliptic functions of x = t 1. It is known that their poles as functions of t 2 move as particles of the elliptic Calogero–Moser model. We extend this correspondence to the level of hierarchies and find the Hamiltonian H k of the elliptic Calogero–Moser model which governs the dynamics of poles with respect to the kth hierarchical time. The Hamiltonians H k are obtained as coefficients of the expansion of the spectral curve near the marked point in which the Baker–Akhiezer function has essential singularity. (paper)
Primary Subject
Source
Available from http://dx.doi.org/10.1088/1751-8121/ac0a31; Country of input: International Atomic Energy Agency (IAEA)
Record Type
Journal Article
Journal
Journal of Physics. A, Mathematical and Theoretical (Online); ISSN 1751-8121;
; v. 54(30); [20 p.]

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Tahir Shah, K.
International Centre for Theoretical Physics, Trieste (Italy)1980
International Centre for Theoretical Physics, Trieste (Italy)1980
AbstractAbstract
[en] When relations are extrapolated beyond their premises of discovery, the operation sometimes results in an undefined object, i.e., one which cannot be identified within the given structure. The thesis is put forth that the occurrence of singularities is due to ''incompleteness'' in knowledge. An intuitive answer on how to deal with singularities (in, for instance, the real number system, space-time, quantum field theory) is presented first. Then a quasi-formalistic approach, e.g. non-standard models in higher-order languages and Lawvere's axiomatic formulation of categories, is set out. The independence of singularity with respect to other primitive notions of the Universe of knowledge is noted
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Source
Dec 1980; 18 p
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Report
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AbstractAbstract
[en] We will study a monodromy preserving deformation with an irregular singular point and determine the τ-function of the monodromy preserving deformation by the elliptic θ-function moving the argument z and the period Ω
Primary Subject
Source
S1751-8113(07)41397-X; Country of input: International Atomic Energy Agency (IAEA)
Record Type
Journal Article
Journal
Journal of Physics. A, Mathematical and Theoretical (Online); ISSN 1751-8121;
; v. 40(39); p. 11939-11960

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