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2014, Springer monographs in mathematics, ISBN 3642388701, xviii, 307 pages
This book provides a detailed and largely self-contained description of various classical and new results on solvability and unsolvability of equations in... 
Differential equations, Linear | Galois theory | Differential algebra | Topological algebras
Book
1991, Translations of mathematical monographs, ISBN 0821845470, Volume 88., viii, 139
Book
Moscow Mathematical Journal, ISSN 1609-3321, 2012, Volume 12, Issue 2, pp. 369 - 396
Journal Article
2013, 2013, ISBN 364238840X, 81
The first part of this book provides an elementary and self-contained exposition of classical Galois theory and its applications to questions of solvability of... 
Field Theory and Polynomials | Algebraic Geometry | Mathematics | Group Theory and Generalizations | Algebra | Topology | Galois theory
eBook
Selecta Mathematica, ISSN 1022-1824, 10/2016, Volume 22, Issue 4, pp. 2099 - 2141
Let G be a complex reductive algebraic group. We study complete intersections in a spherical homogeneous space G / H defined by a generic collection of... 
Spherical variety | Complete intersection | Virtual polytope | Arithmetic and geometric genus | Newton–Okounkov polytope | Primary: 14M27 | Mathematics, general | Moment polytope | Secondary: 14M10 | Mathematics | MATHEMATICS | MATHEMATICS, APPLIED | Newton-Okounkov polytope | BASES | NEWTON POLYTOPES | BODIES | MULTIPLICITIES
Journal Article
St. Petersburg Mathematical Journal, ISSN 1061-0022, 2015, Volume 26, Issue 5, pp. 797 - 811
A set that is a Grobner basis for an ideal with respect to every Grobner ordering is called a universal Grobner basis for that ideal. In the paper, it is... 
Tropical basis | Laurent polynomial | Universal Gröbner basis | Ideal | Seidenberg theorem | MATHEMATICS | universal Grobner basis | ideal | tropical basis
Journal Article
Canadian Mathematical Bulletin, ISSN 0008-4395, 2014, Volume 57, Issue 3, pp. 562 - 572
In a previous paper the authors developed an intersection theory for subspaces of rational functions on an algebraic variety X over k = C. In this short note,... 
Grothendieck group | Intersection number | Cartier divisor | Cartier b-divisor | MATHEMATICS | INTERSECTION THEORY | intersection number
Journal Article
Moscow Mathematical Journal, ISSN 1609-3321, 10/2017, Volume 17, Issue 4, pp. 717 - 740
Let R-Delta (f(1), ... ,f(n+1)) be the Delta-resultant (defined in the paper) of (n + 1)-tuple of Laurent polynomials. We provide an algorithm for computing... 
Poisson formula | Developed system | Laurent polynomial | Parshin reciprocity laws | Resultant | Newton polyhedron | MATHEMATICS | resultant | GROTHENDIECK RESIDUES | MATHEMATICS, APPLIED | developed system
Journal Article
Proceedings of the Steklov Institute of Mathematics, ISSN 0081-5438, 10/2014, Volume 286, Issue 1, pp. 268 - 284
We associate convex regions in ℝ n to m-primary graded sequences of subspaces, in particular m-primary graded sequences of ideals, in a large class of local... 
Mathematics, general | Mathematics | MATHEMATICS | LOCAL-RINGS | MATHEMATICS, APPLIED | Algebra
Journal Article
02/2013
In a previous paper the authors develop an intersection theory for subspaces of rational functions on an algebraic variety X over complex numbers. In this... 
Mathematics - Algebraic Geometry
Journal Article
12/2008
The well-known Bernstein-Kushnirenko theorem from the theory of Newton polyhedra relates algebraic geometry and the theory of mixed volumes. Recently the... 
Mathematics - Algebraic Geometry
Journal Article
MOSCOW MATHEMATICAL JOURNAL, ISSN 1609-3321, 2010, Volume 10, Issue 2, pp. 343 - 375
Let K-rat (X) be the collection of all non-zero finite dimens ional subspaces of rational functions on an n-dimensional irreducible variety X. For any n-tuple... 
MATHEMATICS | linear system on a variety | MATHEMATICS, APPLIED | Cartier divisor | System of algebraic equations | intersection index | mixed volume of convex bodies | Bernstein-Kushirenko theorem
Journal Article
Discrete & Computational Geometry, ISSN 0179-5376, 12/2014, Volume 52, Issue 4, pp. 806 - 823
Journal Article
Proceedings of the Steklov Institute of Mathematics, ISSN 0081-5438, 12/2007, Volume 259, Issue 1, pp. 82 - 100
We discuss the problem of representability and nonrepresentability of algebraic functions by radicals. We show that the Riemann surfaces of functions that are... 
Mathematics, general | Mathematics
Journal Article
Izvestiya: Mathematics, ISSN 1064-5632, 02/2006, Volume 70, Issue 1, pp. 153 - 169
We consider systems of linear partial differential equations with analytic coefficients and discuss existence and uniqueness theorems for their formal and... 
MATHEMATICS | Mathematics | Naturvetenskap | Natural Sciences | Matematik
Journal Article
Mathematical Notes, ISSN 0001-4346, 1/2005, Volume 77, Issue 1, pp. 130 - 139
Journal Article
Proceedings of the Steklov Institute of Mathematics, ISSN 0081-5438, 12/2007, Volume 259, Issue 1, pp. 1 - 5
Article History: 
Mathematics, general | Mathematics
Journal Article
Functional Analysis and Its Applications, ISSN 0016-2663, 1/2001, Volume 35, Issue 1, pp. 52 - 60
In the paper, it is shown that a germ of a many-valued analytic function can be continued analytically along the branching set at least until the topology of... 
Functional Analysis | Analysis | Mathematics | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Arnold Mathematical Journal, ISSN 2199-6792, 3/2016, Volume 2, Issue 1, pp. 121 - 138
A classic result of Ritt describes polynomials invertible in radicals: they are compositions of power polynomials, Chebyshev polynomials and polynomials of... 
Mathematical Physics | Analysis | Mathematics, general | Algebraic Geometry | Mathematics | Solvability in k -radicals | Dynamical Systems and Ergodic Theory | Combinatorics | Topological Galois theory | Exceptional polynomials | Solvability in k-radicals
Journal Article
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