### ?

## Двойные квадрики с большими группами автоморфизмов

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.

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

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

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

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

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

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

Przyjalkowski V., Shramov K., Cheltsov I., 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. ...

Added: January 26, 2019

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

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

Schedrina I., Вопросы философии 2023 № 9 С. 162-166

The article actualizes the historical and philosophical ideas of P.P. Gaidenko in the context of modern problems related to ecology, nature, and man in the surrounding world. The author refers to the concept of types of scientific rationality, emphasizing a unique niche in the history and philosophy of science, which is occupied by the scientific ...

Added: November 15, 2023

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

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

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

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

Kuznetsov A., Prokhorov Y., / Cornell University. Series arXiv "math". 2019.

We give necessary and sufficient conditions for unirationality and rationality of Fano threefolds of geometric Picard rank-1 over an arbitrary field of zero characteristic. ...

Added: August 19, 2020

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

Gorbatov V., Gorbatova Y. V., Вестник Томского государственного университета. Философия. Социология. Политология 2013 № 4(24) С. 11-25

The present paper deals with the modal version of St. Anselm’s ontological argument (the so-called «modal argument», or MA, developed by N. Malcolm and A. Plantinga) and the logic used therein. The authors focus on the problem of conceptual connection between the logic of this argument and some implicit ontological and epistemological assumptions inherent in ...

Added: September 29, 2013

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

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

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

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