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Which quartic double solids are rational?
Journal of Algebraic Geometry. 2019. Vol. 28. P. 201-243.
We study the rationality problem for nodal quartic double solids. In
particular, we prove that nodal quartic double solids with at most six
singular points are irrational and nodal quartic double solids with at
least eleven singular points are rational.
Keywords: rationalityрациональностьQuartic double solidsДвойные пространства с ветвлением в квартике
Publication based on the results of:
Vladimir L. Popov, Journal of the Ramanujan Mathematical Society 2013 Vol. 28A No. Special Issue-2013 dedicated to C.S.Seshadri's 80th birthday P. 409-415
We construct counterexamples to the rationality conjecture regarding the new version of the Makar-Limanov invariant formulated in A. Liendo, G_a-actions of fiber type on affine T-varieties, J. Algebra 324 (2010), 3653--3665. ...
Added: June 20, 2013
Przyjalkowski V., Shramov K., Труды Математического института им. В.А. Стеклова РАН 2016 Т. 294 С. 167-190
We classify three-dimensional nodal Fano varieties that are double covers of smooth quadrics branched over intersections with quartics acted on by finite simple non-abelian groups, and study their rationality. ...
Added: October 13, 2016
Trepalin A., Central European Journal of Mathematics 2014
Let $\bbk$ be a field of characteristic zero and $G$ be a finite group of automorphisms of projective plane over $\bbk$. Castelnuovo's criterion implies that the quotient of projective plane by $G$ is rational if the field $\bbk$ is algebraically closed. In this paper we prove that $\mathbb{P}^2_{\bbk} / G$ is rational for an arbitrary ...
Added: October 14, 2013
Vladimir L. Popov, / Cornell University. Series math "arxiv.org". 2014. No. 1411.6570.
For every algebraically closed field $\boldsymbol k$ of characteristic different from $2$, we prove the following: (1) Generic finite dimensional (not necessarily associative) $\boldsymbol k$-algebras of a fixed dimension, considered up to isomorphism, are parametrized by the values of a tuple of algebraically independent over $\boldsymbol k$ rational functions in the structure constants. ...
Added: November 25, 2014
Andrey S. Trepalin, Central European Journal of Mathematics 2014 Vol. 12 No. 2 P. 229-239
Let $\bbk$ be a field of characteristic zero and $G$ be a finite group of automorphisms of projective plane over $\bbk$. Castelnuovo's criterion implies that the quotient of projective plane by $G$ is rational if the field $\bbk$ is algebraically closed. In this paper we prove that $\mathbb{P}^2_{\bbk} / G$ is rational for an arbitrary ...
Added: December 3, 2013
Galkin S., Shinder E., / Cornell University. Series math "arxiv.org". 2014. No. 1405.5154.
We find a relation between a cubic hypersurface Y and its Fano variety of lines F(Y) in the Grothendieck ring of varieties. We prove that if the class of an affine line is not a zero-divisor in the Grothendieck ring of varieties, then Fano variety of lines on a smooth rational cubic fourfold is birational ...
Added: May 21, 2014
Iliev A., Katzarkov L., Victor Przyjalkowski, Proceedings of the Edinburgh Mathematical Society 2014 Vol. 57 P. 145-173
This paper suggests a new approach to questions of rationality of threefolds based on category theory. Following M. Ballard, D. Favero, L. Katzarkov (ArXiv:1012.0864) and D. Favero, L. Katzarkov (Noether--Lefschetz Spectra and Algebraic cycles, in preparation) we enhance constructions from A. Kuznetsov (arXiv:0904.4330) by introducing Noether--Lefschetz spectra --- an interplay between Orlov spectra (C. Oliva, ...
Added: July 2, 2013
Colliot-Thélène J., Kunyavskiĭ B., Vladimir L. Popov et al., Compositio Mathematica 2011 Vol. 147 No. 2 P. 428-466
Let k be a field of characteristic zero, let G be a connected reductive algebraic group
over k and let g be its Lie algebra. Let k(G), respectively, k(g), be the field of k rational functions on G, respectively, g. The conjugation action of G on itself induces
the adjoint action of G on g. We investigate the ...
Added: March 17, 2013
Popov V., / Bielefeld University. Series LAGRS "Linear Algebraic Groups and Related Structures". 2012. No. 485.
We construct counterexamples to the rationality conjecture regar-ding the new version of the Makar-Limanov invariant introduced in A. Liendo, Ga-actions of fiber type on affine T-varieties, J. Algebra 324 (2010), 3653–3665. ...
Added: January 9, 2013
Kang M., Yuri Prokhorov, Journal of Algebra 2010 Vol. 324 No. 9 P. 2166-2197
Added: December 5, 2013
Bogomolov F. A., Böhning C., Graf von Bothmer H., Central European Journal of Mathematics 2012 Vol. 10 No. 2 P. 466-520
Let G be one of the groups SL n(ℂ), Sp 2n(ℂ), SO m(ℂ), O m(ℂ), or G 2. For a generically free G-representation V, we say that N is a level of stable rationality for V/G if V/G × ℙ N is rational. In this paper we improve known bounds for the levels of stable ...
Added: February 6, 2013
Васильев Д. А., Siberian Mathematical Journal 2023 Vol. 64 No. 3 P. 525-541
We construct an infinite series of irreducible components of the moduli space of stable rank 3 sheaves on P3 with the zero first Chern class and establish the rationality of the components of this series. We also prove the rationality of the irreducible components of the moduli space of stable rank 2 sheaves on P3 belonging to an infinite subseries of the series ...
Added: May 29, 2023
Levin S., В кн. : Рациональность и экзистенция. : СПб. : Философский факультет СПбГУ, 2011. С. 58-61.
Проблема соотношения рациональности и морали имеет долгую историю и богата интерпретациями. Имели место попытки выстроить между этими понятиями иерархические отношения подчинения в духе утилитаризма. Широкое распространение приобрела идея о невозможности объяснения моральных действий рациональностью агента. Иногда стандарты рациональности даже противопоставляется морали. Однако признание автономности сфер рациональности и морали и отказ от сведения их друг другу ...
Added: March 23, 2013
Sushentsova M. S., Журнал институциональных исследований 2017 Т. 9 № 2 С. 46-62
The article represents an overview of general tendencies in interaction between the notions of rationality and morality, and their influence on the foundations of economic coordination. Firstly, two main directions of evolution of rationality model are considered: the theory of perspectives of D. Kahneman and A. Tverski (the empirical restriction) and economic imperialism of G. ...
Added: August 24, 2018
Makeeva L. B., , in : Rationality in Action: Intentions, Interpretations and Interactions. : St. Petersburg : Aletheya, 2015. P. 110-114.
The purpose of the present paper is to describe and evaluate recent Bayesian developments concerning the theory of confirmation and the theory of scientific reasoning as a whole. It is argued that the Bayesian approach in contemporary philosophy of science has, as its main consequence, a serious revision of the conception of scientific rationality. ...
Added: November 2, 2015
Shamarina E., В кн. : Третий Международный Конгресс Русского общества истории и философии науки «ПОСЛЕ ПОСТПОЗИТИВИЗМА». Сборник научных статей. : М. : Издательство РОИФН, 2022. С. 681-684.
Michael Friedman made an attempt to combine Kantian transcendental philosophy and Kuhn's historiographical model in a view of changes in science. His idea of a rational revision of scientific principles contrasts with Kuhn's idea of the existence of universal sets of values that ensure scientific progress. Friedman appeals to philosophical developments of the metatheoretical level ...
Added: December 23, 2023
Rezvykh P. V., Вестник Российского университета дружбы народов. Серия: Философия 2013 № 1 С. 6-18
The article gives an analysis of the relation between freedom and rationality in the work of F.W.J.Schelling in the time between 1800 and 1810. The author argues that Schelling’s understanding of the concept of freedom in context of his identity philosophy is not so due to his reception of Platonism as to his reflection on ...
Added: November 3, 2013
Prokhorov Y., Kuznetsov A., / Cornell University. Series arXiv "math". 2020.
We discuss birational properties of Mukai varieties, i.e., of higher-dimensional analogues of prime Fano threefolds of genus g∈{7,8,9,10} over an arbitrary field 𝗄 of zero characteristic. In the case of dimension n≥4 we prove that these varieties are 𝗄-rational if and only if they have a 𝗄-point except for the case of genus 9, where we assume n≥5. Furthermore, we prove that Mukai varieties of ...
Added: August 19, 2020
Gorbatova Y. V., Философия. Журнал Высшей школы экономики 2018 Т. 2 № 4 С. 167-178
В этой работе автор анализиурет замечания и идеи своих коллег, высказанные в процессе панельной дискуссии. Работа не подводит итоги, но, скорее, рассматривает вновь открывшиеся перспективы для более глубокого обсуждения и обдумывания тем, заданных фокусной статьей и ответами на нее. ...
Added: January 10, 2019
Grebnev L., Terra Economicus 2013 Т. 11 № 2 С. 136-151
Accounts of several authoritative in-troductory textbooks are compared, the notions under consideration are: uncertainty, optimization, marginal items, interests. Proceeding from this basis, the author's classification of subjects’ objective interests is made; two fundamental principles of economic rationality – one of cost minimization and the other of benefit maximi-zation, – are described, with their associations to ...
Added: October 21, 2013
Rozmainsky I. V., Економiчний Вiсник Донбасу 2012 № 4(22) С. 34-42
Heterodox – Post Keynesian and Institutionalist - economics proves that expansion of financial sector can be harmful for the real sector. Such conclusion is an effect of account of variability of preferences, planning horizons and degree of rationality in the behavior of economic agents. We suppose that both methodology and conclusions of Heterodox Economics can ...
Added: December 26, 2012
Щербина В. В., Popova E. P., Личность. Культура. Общество 2016 Т. XVIII № 1-2 (89-90) С. 106-118
The article is devoted to the origins, theoretical and methodological foundations, problems and prospects of activities related to the streamlining of management in business organizations. It answers the question whether the activities to streamline management in business organizations prospects in modern conditions, and if so, why and in what forms.
This is the third (the final) ...
Added: September 25, 2016
Levin S., В кн. : Философия. Язык. Культура (вып.4). Вып. 4.: СПб. : Алетейя, 2013. С. 135-144.
В статье критически реконструируется аргументация Дж. Сёрла в пользу того, что для каждого лингвистически компетентного субъекта существуют логическое требование сильного альтруизма. Благодаря тому, что для обоснования моральных действий Сёрл обращается только к внутренним ресурсам субъекта, его подход сулит возможность преодолеть разрыв между сущим и должным. Тем не менее, в условиях очевидной вариативности этических мотивов и ...
Added: January 4, 2014
Dobrohotov A. L., В кн. : Следование правилу: рассуждение, разум, рациональность. : СПб. : Алетейя, 2014. С. 134-150.
The search for the Russian philosophy of its own way of understanding “Self” have identified and detected in the presented concepts. They imply that the philosophy of the Silver Age sought to recapture part of the "territory" of the irrational and to extend the concept of the rational by reviewing the nature and assessment of ...
Added: November 16, 2014