scientific article; zbMATH DE number 773851
From MaRDI portal
Publication:4838935
zbMath0829.14002MaRDI QIDQ4838935
James Alexander, Andre Hirschowitz
Publication date: 22 January 1996
Title: zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Singularities in algebraic geometry (14B05) Polynomial rings and ideals; rings of integer-valued polynomials (13F20) Polynomials in general fields (irreducibility, etc.) (12E05) Approximation by polynomials (41A10) Automorphisms of curves (14H37)
Related Items
Generic power sum decompositions and bounds for the Waring rank, Real rank geometry of ternary forms, Polynomial foldings and rank of tensors, The Alexander–Hirschowitz Theorem and Related Problems, Segre Functions in Multiprojective Spaces and Tensor Analysis, On the secant varieties of tangential varieties, Quantum algorithm for multivariate polynomial interpolation, Secant varieties of Segre-Veronese embeddings of \((\mathbb{P }^1)^r\), On the real rank of monomials, Dimensional Differences Between Faces of the Cones of Nonnegative Polynomials and Sums of Squares:, Generating polynomials and symmetric tensor decompositions, On projective embeddings of generic rational surfaces, Secant varieties of Grassmann varieties, Waring-like decompositions of polynomials. I., Topology of tensor ranks, The degree of the tangent and secant variety to a projective surface, A bound for the Waring rank of the determinant via syzygies, On the identifiability of ternary forms, Tropical approach to Nagata's conjecture in positive characteristic, Actual and virtual dimension of codimension \(2\) general linear subspaces in \(\mathbb{P}^n\), The multidimensional truncated moment problem: the moment cone, Secant varieties of the varieties of reducible hypersurfaces in \(\mathbb{P}^n\), Algebraic geometry and representation theory in the study of matrix multiplication complexity and other problems in theoretical computer science, A New Bound for the Waring Rank of Monomials, Most secant varieties of tangential varieties to Veronese varieties are nondefective, Geometry and the complexity of matrix multiplication, Ranks and symmetric ranks of cubic surfaces, On the strong Lefschetz problem for uniform powers of general linear forms in 𝑘[𝑥,𝑦,𝑧], Identifiability for a class of symmetric tensors, Zero-dimensional complete intersections and their linear span in the Veronese embeddings of projective spaces, Low Rank Symmetric Tensor Approximations, A classification of the weak Lefschetz property for almost complete intersections generated by uniform powers of general linear forms, Three decompositions of symmetric tensors have similar condition numbers, The monic rank, The Condition Number of Join Decompositions, On Waring's problem for systems of skew-symmetric forms, On generic identifiability of symmetric tensors of subgeneric rank, Enumerating number fields, Waring problems and the Lefschetz properties, $K3$ surfaces of genus 8 and varieties of sums of powers of cubic fourfolds, A brief proof of a maximal rank theorem for generic double points in projective space, Generic forms of low Chow rank, Linear subspaces, symbolic powers and Nagata type conjectures, On base loci of higher fundamental forms of toric varieties, Barriers for Rank Methods in Arithmetic Complexity, On the Hilbert function of general fat points in \(\mathbb{P}^1\times\mathbb{P}^1\), An upper bound for the Waring rank of a form, On minimal decompositions of low rank symmetric tensors, A tropical approach to secant dimensions, Algebraic boundaries among typical ranks for real binary forms of arbitrary degree, Expected term bases for generic multivariate Hermite interpolation, The Waring rank of binary binomial forms, Kähler differentials for fat point schemes in \(\mathbb{P}^1\times\mathbb{P}^1\), On non-secant defectivity of Segre-Veronese varieties, Curvilinear schemes and maximum rank of forms, On the Alexander-Hirschowitz theorem, Varieties of completely decomposable forms and their secants, Linear subspaces of symmetric tensors whose non-zero elements have at least a prescribed rank, Apolarity for determinants and permanents of generic matrices, On the secant varieties to the tangent developable of a Veronese variety, Power sum decompositions of defining equations of reflection arrangements, On the weak non-defectivity of Veronese embeddings of projective spaces, On the first infinitesimal neighborhood of a linear configuration of points in \(\mathbb P^2\), On the secant varieties to the tangential varieties of a Veronesean, Base loci of linear systems and the Waring problem, Induction for secant varieties of Segre varieties, Remarks on the Symmetric Rank of Symmetric Tensors, Most boson quantum states are almost maximally entangled, Reconstruction algorithms for sums of affine powers, Orthogonal tensor decomposition and orbit closures from a linear algebraic perspective, On maximum, typical and generic ranks, Representations of homogeneous polynomials as a sum of powers of linear forms with restricted support, Large families of homogeneous polynomials with non-unique additive decompositions, Quartic unexpected curves and surfaces, How to integrate a polynomial over a simplex, Hilbert functions of schemes of double and reduced points, Secant varieties of ℙ¹×⋯×ℙ¹ (𝕟-times) are NOT defective for 𝕟≥5, Tangential varieties of Segre-Veronese surfaces are never defective, Monomials as sums of powers: The real binary case, Algebraic stories from one and from the other pockets, Efficient Evaluation of Noncommutative Polynomials Using Tensor and Noncommutative Waring Decompositions, Homotopy techniques for tensor decomposition and perfect identifiability, On the X-rank with respect to linear projections of projective varieties, All secant varieties of the Chow variety are nondefective for cubics and quaternary forms, Numerical implicitization: a Macaulay2 package, Equations and syzygies of the first secant variety to a smooth curve, Singularities of linear systems and the Waring problem, The Hitchhiker guide to: secant varieties and tensor decomposition, Upper bounds on number fields of given degree and bounded discriminant, Binary decompositions and varieties of sums of binaries, Progress on the symmetric Strassen conjecture, On linear systems with multiple points on a rational normal curve, Homogeneous projective varieties with semi-continuous rank function, On secant defectiveness and identifiability of Segre-Veronese varieties, Kähler differentials and Kähler differents for fat point schemes, Numerical optimization for symmetric tensor decomposition, Waring and cactus ranks and strong Lefschetz property for annihilators of symmetric forms, Typical real ranks of binary forms, Minimality and uniqueness for decompositions of specific ternary forms, Waring loci and the Strassen conjecture, Dimension of Marginals of Kronecker Product Models, Effective Criteria for Specific Identifiability of Tensors and Forms, Decomposition Algorithms for Tensors and Polynomials, The Hilbert function of general unions of lines, double lines and double points in projective spaces, On the description of identifiable quartics, Identifiability of an X-Rank Decomposition of Polynomial Maps, Identifiability for mixtures of centered Gaussians and sums of powers of quadratics, Computing Geometric Feature Sizes for Algebraic Manifolds, Dimension of tensor network varieties, Binary forms of suprageneric rank and the multiple root loci, Generalizations of the Schrödinger maximal operator: building arithmetic counterexamples, Waring identifiability for powers of forms via degenerations, A counterexample to a conjecture on simultaneous Waring identifiability, A Footnote to a Footnote to a Paper of B. Segre, Unnamed Item, The structure and free resolutions of the symbolic powers of star configurations of hypersurfaces, On bounding the number of generators for fat point ideals on the projective plane, Fat points schemes on a smooth quadric, Canonical curves and varieties of sums of powers of cubic polynomials., Power sum decompositions of elementary symmetric polynomials, Partially Symmetric Variants of Comon's Problem Via Simultaneous Rank, Ranks and Singularities of Cubic Surfaces, Special apolar subset: the case of star configurations, Decoupling Multivariate Polynomials Using First-Order Information and Tensor Decompositions, Entanglement classification with algebraic geometry, The secant line variety to the varieties of reducible plane curves, Strict inclusions of high rank loci, Unexpected hypersurfaces with multiple fat points, The asymptotic leading term for maximum rank of ternary forms of a given degree, Algebraic methods in approximation theory, On regularity of generalized Hermite interpolation, An algorithm to bound the regularity and nonemptiness of linear systems in \(\mathbb P^n\), Set evincing the ranks with respect to an embedded variety (symmetric tensor rank and tensor rank), A very brief introduction to nonnegative tensors from the geometric viewpoint, Seeking for the maximum symmetric rank, On singularities of third secant varieties of Veronese embeddings, Postulation of general unions of lines and double points in a higher dimensional projective space, Some examples of forms of high rank, A Gröbner basis for the secant ideal of the second hypersimplex, On linear systems of \(\mathbb P^3\) with nine base points, Maximal rank for planar singularities of multiplicity 2, A probabilistic algorithm for the secant defect of Grassmann varieties, Mini-workshop: Ideals of linear subspaces, their symbolic powers and Waring problems. Abstracts from the mini-workshop held February 15--21, 2015., Smooth points of \(\text{Gor}(T)\), On non-defectivity of certain Segre-Veronese varieties, Computing symmetric rank for symmetric tensors, Cones of effective divisors on the blown-up \({\mathbb {P}}^3\) in general lines, Symmetric tensor rank over an infinite field, On the number of Waring decompositions for a generic polynomial vector, Generic hypersurface singularities, Eigenvectors of tensors and algorithms for Waring decomposition, Tensor decomposition and homotopy continuation, High-rank ternary forms of even degree, On the variety parameterizing completely decomposable polynomials, Effective identifiability criteria for tensors and polynomials, Postulation of general quintuple fat point schemes in \(\mathbb P^3\), Inverse systems of zero-dimensional schemes in \(\mathbb P^n\), 16,051 formulas for Ottaviani's invariant of cubic threefolds, Secants of Lagrangian Grassmannians, On the rank of a binary form, On the dimension of higher secant varieties of Segre varieties \(\mathbb P^n \times \cdots \times \mathbb P^n\), On the maximum rank of a real binary form, On polynomials with given Hilbert function and applications, On the dimensions of secant varieties of Segre-Veronese varieties, On the secant varieties to the osculating variety of a Veronese surface, A criterion for detecting the identifiability of symmetric tensors of size three, On Segre's bound for fat points in \(\mathbb{P}^n\), The solution to the Waring problem for monomials and the sum of coprime monomials, The discriminant of a cubic surface, The multidimensional truncated moment problem: Carathéodory numbers, Decomposition of homogeneous polynomials with low rank, New examples of defective secant varieties of Segre-Veronese varieties, Canonical curves with low apolarity, On generic and maximal \(k\)-ranks of binary forms, Higher secant varieties of \(\mathbb P^n \times \mathbb P^n\) embedded in bi-degree \((1,d)\), Postulation of generic lines and one double line in \(\mathbb {P}^n\) in view of generic lines and one multiple linear space, 3-dimensional sundials, The symbolic defect of an ideal, A new proof of the Alexander-Hirschowitz interpolation theorem, On the typical rank of real polynomials (or symmetric tensors) with a fixed border rank, Dimensions of group-based phylogenetic mixtures, Lower bound for ranks of invariant forms, On a geometric method for the identifiability of forms, On the locus of points of high rank, Lower bounds by Birkhoff interpolation, On real typical ranks, Spaces of sums of powers and real rank boundaries, Vanishing theorems for linearly obstructed divisors, Waring decompositions and identifiability via Bertini and Macaulay2 software, The role of the cotangent bundle in resolving ideals of fat points in the plane, On the Waring rank of binary forms, Bounds on the tensor rank, On the ranks and border ranks of symmetric tensors, Zero-dimensional subschemes of ruled varieties, On partial polynomial interpolation, Examples of \(k\)-regular maps and interpolation spaces, Special effect varieties and \((-1)\)-curves, Postulation of general unions of lines and multiplicity two points in \(\mathbb P^3\), Interpolation and parallel lines, The geometric interpretation of Fröberg-Iarrobino conjectures on infinitesimal neighbourhoods of points in projective space, Rank-\(r\) decomposition of symmetric tensors, Semialgebraic sets and real binary forms decompositions, Bipolynomial Hilbert functions, VSPs of cubic fourfolds and the Gorenstein locus of the Hilbert scheme of 14 points on \(\mathbb{A}^6\), Moment identifiability of homoscedastic Gaussian mixtures, On the Hartshorne-Hirschowitz theorem, Unexpected surfaces singular on lines in \(\mathbb{P}^3\), On the Terracini locus of projective varieties, Postulation of general quartuple fat point schemes in \(\mathbb{P}^3\), Hilbert polynomials of Kähler differential modules for fat point schemes, Secant varieties to osculating varieties of Veronese embeddings of \(\mathbb P^n\), Generic and typical ranks of multi-way arrays, Higher infinitesimal neighbourhoods, On secant dimensions and identifiability of flag varieties, Riemannian Newton optimization methods for the symmetric tensor approximation problem, The Lefschetz question for ideals generated by powers of linear forms in few variables, Uniform matrix product states from an algebraic geometer's point of view, Waring rank of binary forms, harmonic cross-ratio and golden ratio, High-order vanishing ideals at \(n+3\) points of \(\mathbb{P}^n\), Almost all subgeneric third-order Chow decompositions are identifiable, Secant non-defectivity via collisions of fat points, The minimal free resolution for the first infinitesimal neighborhoods of \(n\) general points in the plane, Ranks of tensors, secant varieties of Segre varieties and fat points, Numerical degeneracy of two families of rational surfaces, Surfaces in \({\mathbb P}^4\) with extremal general hyperplane section.