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Symmetry, Integrability and Geometry: Methods and Applications, ISSN 1815-0659, 03/2020
SIGMA 16 (2020), 016, 12 pages We prove a version of the BKK theorem for the ring of conditions of a spherical homogeneous space $G/H$. We also introduce the... 
Mathematics - Algebraic Geometry
Journal Article
RUSSIAN MATHEMATICAL SURVEYS, ISSN 0036-0279, 2018, Volume 73, Issue 5, pp. 935 - 939
Journal Article
03/2018
The purpose of this note is to give an exposition of some interesting combinatorics and convex geometry concepts that appear in algebraic geometry in relation... 
Mathematics - Algebraic Geometry
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
RUSSIAN MATHEMATICAL SURVEYS, ISSN 0036-0279, 2016, Volume 71, Issue 6, pp. 1153 - 1157
Journal Article
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
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
Izvestiya Mathematics, ISSN 1064-5632, 2016, Volume 80, Issue 1, pp. 263 - 284
We calculate the number of irreducible components of varieties in (C*)(n) determined by generic systems of equations with given Newton polytopes. Every such... 
Irreducible components | Newton polytopes | Holomorphic forms | Mixed volume | MATHEMATICS | irreducible components | mixed volume | holomorphic forms | Polytopes | Intersections | Mathematical analysis | Invariants
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
St. Petersburg Mathematical Journal, ISSN 1061-0022, 10/2015, Volume 26, Issue 5, p. 797
öööötropical Noetherity of a ring of Laurent polynomials. This theorem is close to the existence theorem for a universal basis and is needed for the in , which... 
Journal Article
06/2015
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 sections... 
Mathematics - Algebraic Geometry
Journal Article
Functional Analysis and its Applications, ISSN 0016-2663, 2015, Volume 49, Issue 1, pp. 50 - 56
Liouville's theorem describes algebraic functions integrable in terms of generalized elementary functions. In many cases, algorithms based on this theorem make... 
solvability in finite terms | algebraic function | Abelian integral | elementary function | MATHEMATICS | MATHEMATICS, APPLIED | Algorithms
Journal Article
Discrete & Computational Geometry, ISSN 0179-5376, 12/2014, Volume 52, Issue 4, pp. 806 - 823
Journal Article
Scientific and Technical Information Processing, ISSN 0147-6882, 12/2014, Volume 41, Issue 5, pp. 293 - 301
The problem of comparing digitized (scanned) images is described. The paper provides a theoretical solution of the problem of searching for the parallel... 
optimal position of figures | image | Computer Systems Organization and Communication Networks | function of comparison | shift of images | Computer Science | Digital imaging | Algorithms | Computation | Searching | Symbols | Images | Digitization | Boundaries | Transport | Standards | Optimization
Journal Article
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
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
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
RUSSIAN MATHEMATICAL SURVEYS, ISSN 0036-0279, 2014, Volume 69, Issue 4, pp. 743 - 751
Journal Article
MOSCOW MATHEMATICAL JOURNAL, ISSN 1609-3321, 04/2014, Volume 14, Issue 2, pp. 173 - 179
Journal Article
10/2013
Let R be the local ring of a point on a variety X over an algebraically closed field k. We make a connection between the notion of mixed (Samuel) multiplicity... 
Journal Article
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