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## An Infinite Series of Rational Components of the Moduli Space of Rank 3 Sheaves on P3

Siberian Mathematical Journal. 2023. Vol. 64. No. 3. P. 525–541.

Васильев Д. А.

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 of irreducible components described by Jardim, Markushevich, and Tikhomirov.

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

Alexandrov A., Basalaev A., Buryak A., International Mathematics Research Notices 2023 Vol. 2023 No. 17 P. 14840–14889

We present a construction of an open analogue of total descendant and total ancestor potentials via an “open version” of Givental’s action. Our construction gives a genus expansion for an arbitrary solution to the open WDVV equations satisfying a semisimplicity condition and admitting a unit. We show that the open total descendant potentials we define ...

Added: September 14, 2022

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

Roman Avdeev, Cupit-Foutou S., Transformation Groups 2018 Vol. 23 No. 2 P. 299–327

We give a combinatorial description of all affine spherical varieties with prescribed weight monoid Γ. As an application, we obtain a characterization of the irreducible components of Alexeev and Brion’s moduli scheme M_Γ for such varieties. Moreover, we find several sufficient conditions for M_Γ to be irreducible and exhibit several examples where M_Γ is reducible. ...

Added: October 17, 2017

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

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

Брауэр О., Buryak A., Функциональный анализ и его приложения 2021 Т. 55 № 4 С. 22–39

In a recent paper, given an arbitrary homogeneous cohomological field theory (CohFT), Rossi, Shadrin, and the first author proposed a simple formula for a bracket on the space of local functionals, which conjecturally gives a second Hamiltonian structure for the double ramification hierarchy associated to the CohFT. In this paper we prove this conjecture in ...

Added: September 14, 2022

Buryak A., Hernandez Iglesias F., Shadrin S., Epijournal de Geometrie Algebrique 2022 Vol. 6 Article 8595

We propose a conjectural formula for DR_g(a,−a)\lambda_g and check all its expected properties. Our formula refines the one point case of a similar conjecture made by the first named author in collaboration with Guéré and Rossi, and we prove that the two conjectures are in fact equivalent, though in a quite non-trivial way. ...

Added: September 14, 2022

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

Buryak A., Clader E., Tessler R., Journal of Geometry and Physics 2023 Vol. 192 Article 104960

In our previous two papers, we constructed an r-spin theory in genus zero for Riemann surfaces with boundary and fully determined the corresponding intersection numbers, providing an analogue of Witten's r-spin conjecture in genus zero in the open setting. In particular, we proved that the generating series of open r-spin intersection numbers is determined by the genus-zero part ...

Added: November 20, 2023

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

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

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

Buryak A., Gubarevich D., Mathematical Physics Analysis and Geometry 2023 Vol. 26 No. 3 Article 23

One of many manifestations of a deep relation between the topology of the moduli spaces of algebraic curves and the theory of integrable systems is a recent construction of Arsie, Lorenzoni, Rossi, and the first author associating an integrable system of evolutionary PDEs to an F-cohomological field theory (F-CohFT), which is a collection of cohomology ...

Added: November 20, 2023

Arsie A., Buryak A., Lorenzoni P. et al., Communications in Mathematical Physics 2023 Vol. 397 P. 141–197

In this paper, we generalize the Givental theory for Frobenius manifolds and cohomological field theories to flat F-manifolds and F-cohomological field theories. In particular, we define a notion of Givental cone for flat F-manifolds, and we provide a generalization of the Givental group as a matrix loop group acting on them. We show that this action is transitive on semisimple flat F-manifolds. We then extend this ...

Added: December 8, 2022

Buryak A., Netser Zernik A., Pandharipande R. et al., Advances in Mathematics 2022 Vol. 401 Article 108249

We define stationary descendent integrals on the moduli space of stable maps from disks to (CP^1,RP^1). We prove a localization formula for the stationary theory involving contributions from the fixed points and from all the corner-strata. We use the localization formula to prove a recursion relation and a closed formula for all genus 0 disk cover ...

Added: September 14, 2022

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

Buryak A., Rossi P., Bulletin of the London Mathematical Society 2021 Vol. 53 No. 3 P. 843–854

In this paper we compute the intersection number of two double ramification (DR) cycles (with different ramification profiles) and the top Chern class of the Hodge bundle on the moduli space of stable curves of any genus. These quadratic DR integrals are the main ingredients for the computation of the DR hierarchy associated to the ...

Added: February 1, 2021

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

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

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

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

Porus V. N., Russian Studies in Philosophy 2017 Vol. 55 No. 5 P. 320–335

Leo Tolstoy’s Moralism is a call for the purification of moral universals as the foundations of culture, in which there is no contradiction between the values of an individual life and the values of the social “world.” A “moralist preacher” must fulfill two main requirements. First, he must personally fulfill the principles of his teaching. ...

Added: November 10, 2017