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14 July 2017

Universities as Innovation Drivers

The latest issue of the Foresight Journal (vol. 11. No. 2), published as a special issue, looks at various aspects of integrating universities’ educational, research, and innovative activities in a ‘knowledge triangle.’ Experts from Austria, Indonesia, Iran, Russia, Sweden, and the UK, as well as representatives of the OECD had the opportunity to share their knowledge in this field.

14 June 2017

New Publication by HSE Lecturer Yury Kabanov Explores the Politics of Open Data in Russia

The article “Politics of Open Data in Russia: Regional and Municipal Perspectives”,  co-authored by our colleague from the Department of Political Science Yury Kabanov, was published in the « E-Democracy for Smart Cities» chapter of the Springer Journal this May.

1 June 2017

New Issue of HERB Focuses on International Students

In recent discussion on internationalisation, the role of international students as main drivers has been rightly reconsidered. The 12th issue of Higher Education and Beyond addresses the importance of international students for higher educational institutions and the change they bring.

Book chapter

Bass' triangulability problem

P. 425-441.
Vladimir L. Popov.

Exploring Bass’ Triangulability Problem on unipotent algebraic
subgroups of the affine Cremona groups, we prove a triangulability
criterion, the existence of nontriangulable connected solvable affine algebraic
subgroups of the Cremona groups, and stable triangulability
of such subgroups; in particular, in the stable range we answer Bass’
Triangulability Problem in the affirmative. To this end we prove a theorem
on invariant subfields of 1-extensions. We also obtain a general
construction of all rationally triangulable subgroups of the Cremona
groups and, as an application, classify rationally triangulable connected
one-dimensional unipotent affine algebraic subgroups of the Cremona
groups up to conjugacy.











Language: English
 Text on another site
Keywords: algebraic variety automorphism group

In book

Advanced Studies in Pure Mathematics
Vol. 75: Algebraic Varieties and Automorphism Groups. The Mathematical Society of Japan, 2017.
Similar publications
Advanced Studies in Pure Mathematics
Vol. 75: Algebraic Varieties and Automorphism Groups. The Mathematical Society of Japan, 2017.
Added: Jul 12, 2017
Rationality and the FML invariant
Popov V. L. Linear Algebraic Groups and Related Structures. LAGRS. Bielefeld University, 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: Jan 9, 2013
On the Local Structure Theorem and equivariant geometry of cotangent bundles
Zhgoon V. Journal of Lie Theory. 2013. Vol. 23. P. 607-638.

Let $G$ be a connected reductive group acting on an irreducible normal algebraic variety $X$. We give a slightly improved version of  Local Structure Theorems obtained by Knop and Timashev, which describe the action of some parabolic subgroup of $G$ on an open subset of  $X$. We also extend various results of Vinberg and Timashev on the set of horospheres in $X$.  We construct a family of nongeneric horospheres in $X$ and a variety $\Hor$ parameterizing this family, such that there is  a rational  $G$-equivariant symplectic covering  of cotangent vector bundles $T^*\Hor \dashrightarrow T^*X$. As an application we recover the  description of the image of the moment map of $T^*X$ obtained by Knop.   In our proofs we use only geometric  methods  which do not involve differential operators.

Added: Feb 6, 2013
Classification of Algebraic Varieties
Zürich: European Mathematical Society Publishing house, 2010.

Fascinating and surprising developments are taking place in the classification of algebraic varieties. Work of Hacon and McKernan and many others is causing a wave of breakthroughs in the Minimal Model Program: we now know that for a smooth projective variety the canonical ring is finitely generated. These new results and methods are reshaping the field. Inspired by this exciting progress, the editors organized a meeting at Schiermonnikoog and invited leading experts to write papers about the recent developments. The result is the present volume, a lively testimony of the sudden advances that originate from these new ideas. This volume will be of interest to a wide range of pure mathematicians, but will appeal especially to algebraic and analytic geometers.

Added: Oct 11, 2013
On families of lagrangian tori on hyperkaehler manifolds
Amerik E., Campana F. algebraic geometry. arxiv.org. Cornell University library, 2013
This is a note on Beauville's problem (solved by Greb, Lehn and Rollenske in the non-algebraic case and by Hwang and Weiss in general) whether a lagrangian torus on an irreducible holomorphic symplectic manifold is a fiber of a lagrangian fibration. We provide a different, very short solution in the non-algebraic case and make some observations suggesting a different approach in the algebraic case.
Added: Apr 9, 2013
Descent theory for semiorthogonal decompositions
Elagin A. D. Sbornik Mathematics. 2012. Vol. 203. No. 5. P. 645-676.

We put forward a method for constructing semiorthogonal decompositions of the derived category of G-equivariant sheaves on a variety X under the assumption that the derived category of sheaves on X admits a semiorthogonal decomposition with components preserved by the action of the group G on X. This method is used to obtain semiorthogonal decompositions of equivariant derived categories for projective bundles and blow-ups with a smooth centre as well as for varieties with a full exceptional collection preserved by the group action. Our main technical tool is descent theory for derived categories.

Added: Feb 4, 2013
Birational splitting and algebraic group actions
Vladimir L. Popov. arxiv.org. math. Cornell University, 2015. No. 1502.02167.
According to the classical theorem, every irreducible algebraic variety endowed with a nontrivial rational action of a connected linear algebraic group is birationally isomorphic to a product of another algebraic variety and the s-dimensional projectice space with positive s. We show that the classical proof of this theorem actually works only in characteristic 0 and we give a characteristic free proof of it. To this end we prove and use a characterization of connected linear algebraic groups G with the property that every rational action of G on an irreducible algebraic variety is birationally equivalent to a regular action of G on an affine algebraic variety.
Added: Feb 10, 2015
On infinite dimensional algebraic transformation groups
Vladimir L. Popov. Transformation Groups. 2014. Vol. 19. No. 2. P. 549-568.

We explore orbits, rational invariant functions, and quotients of the natural actions of connected, not necessarily finite dimensional subgroups of the automorphism groups of irreducible algebraic varieties. The applications of the results obtained are given.

Added: Mar 17, 2014