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

Differential equations, Linear | Galois theory | Differential algebra | Topological algebras

Book

2012, Reviews in mathematics and mathematical physics, ISBN 1904868983, Volume 14, part 2, xxiii, 92

Book

3.
Fewnomials

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

We associate convex bodies to a wide class of graded G-algebras where G is a connected reductive group. These convex bodies give information about the Hilbert...

Graded G-algebra | Multiplicity of | Line bundle | Convex body | Representation | Volume of | Mixed volume | Semigroup of integral points | Duistermaat-Heckman measure | G-line bundle | Brunn-Minkowski inequality | Moment map | Reductive group action | MATHEMATICS, APPLIED | REPRESENTATIONS | graded G-algebra | volume of a line bundle | VOLUME | VARIETIES | NEWTON POLYHEDRA | semigroup of integral points | MULTIPLICITIES | MATHEMATICS | moment map | multiplicity of a representation | mixed volume | convex body

Graded G-algebra | Multiplicity of | Line bundle | Convex body | Representation | Volume of | Mixed volume | Semigroup of integral points | Duistermaat-Heckman measure | G-line bundle | Brunn-Minkowski inequality | Moment map | Reductive group action | MATHEMATICS, APPLIED | REPRESENTATIONS | graded G-algebra | volume of a line bundle | VOLUME | VARIETIES | NEWTON POLYHEDRA | semigroup of integral points | MULTIPLICITIES | MATHEMATICS | moment map | multiplicity of a representation | mixed volume | convex body

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

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

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

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

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

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

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

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

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

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

If the complement of a closed convex set in a closed convex cone is bounded, then this complement minus the apex of the cone is called a coconvex set. Coconvex...

Virtual convex polytopes | Computational Mathematics and Numerical Analysis | Aleksandrov-Fenchel inequalities | Volume | Valuations on polytopes | Mathematics | Combinatorics | Coconvex bodies | MATHEMATICS | POLYTOPES | COMPUTER SCIENCE, THEORY & METHODS | INTEGRAL-POINTS | Valuation | Algebra | Geometry | Polytopes | Theorems | Integers | Computational geometry | Singularities | Apexes | Inequalities | Complement | Invariants

Virtual convex polytopes | Computational Mathematics and Numerical Analysis | Aleksandrov-Fenchel inequalities | Volume | Valuations on polytopes | Mathematics | Combinatorics | Coconvex bodies | MATHEMATICS | POLYTOPES | COMPUTER SCIENCE, THEORY & METHODS | INTEGRAL-POINTS | Valuation | Algebra | Geometry | Polytopes | Theorems | Integers | Computational geometry | Singularities | Apexes | Inequalities | Complement | Invariants

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

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

MATHEMATICS | Mathematics | Naturvetenskap | Natural Sciences | Matematik

Journal Article

Mathematical Notes, ISSN 0001-4346, 1/2005, Volume 77, Issue 1, pp. 130 - 139

Systems of linear partial differential equations with constant coefficients are considered. The spaces of formal and analytic solutions of such systems are...

space of analytic solutions | Mathematics, general | Hilbert polynomial | Mathematics | symbol of a system | Hilbert—Samuel polynomial | system of linear partial differential equations | space of formal solutions | Symbol of a system | Hilbert-Samuel polynomial | Space of analytic solutions | System of linear partial differential equations | Space of formal solutions | MATHEMATICS

space of analytic solutions | Mathematics, general | Hilbert polynomial | Mathematics | symbol of a system | Hilbert—Samuel polynomial | system of linear partial differential equations | space of formal solutions | Symbol of a system | Hilbert-Samuel polynomial | Space of analytic solutions | System of linear partial differential equations | Space of formal solutions | MATHEMATICS

Journal Article

Proceedings of the Steklov Institute of Mathematics, ISSN 0081-5438, 12/2007, Volume 259, Issue 1, pp. 1 - 5

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

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

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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