On Waring’s problem for several algebraic forms

By Enrico Carlini, J. Chipalkatti. 2003

63 citations recorded by the source corpus.

Subfields: Computational Mathematics, Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/04b4e188f50bc9d2e4294989c18843d2eb4e6ff8

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In Computational Mathematics

In Computational Theory and Mathematics

In Geometry and Topology

Citations in the corpus

Representation Theory and Projective Geometry (2002, background): “hrased geometrically, the problem is to ﬁnd the minimal ksuch that σ k(v d(Pn)) = P(SdCn+1). This problem was solved by Alexander and Hirschowitz [1]. Generalizations and variants are still open, see [13, 47, 75] for recent progress. 2.7. Tits correspondences and applications. In §2.7.1 we describe ”
Ranks of tensors and a generalization of secant varieties (2009, background): “ of endomorphisms, exactly the expression that the endomorphisms commute (see [4, 29] for discussions). Remark 1.2. Grassmann secant varieties have recently appeared in [7], [10], [13], [9], [8], and [5]. These articles are primarily interested in studying the dimension of σr,k(X), especially in the”
The Hitchhiker Guide to: Secant Varieties and Tensor Decomposition (2018, background): “The above conjectures are based on results that can be found in [123, 131, 93, 128, 99, 122, 126, 130, 112, 129, 134, 125, 124, 132, 133, 127, 121].”
ON THE LENGTH OF BINARY FORMS (2010, background): “The interested reader is directed to [4, 5, 10, 12, 13, 17, 20, 23, 29, 39, 40, 41] as representative recent works.”
On the dimensions of secant varieties of Segre-Veronese varieties (2009, unknown): “Defective secant varieties of Segre-Veronese varieties are, however, less well-understood, although considerable efforts have been already made to complete the list of such varieties (see for example, [18], [16], [8], [14], [27], [6]).”
Classical Algebraic Geometry: A Modern View (2012, background): “There are no exceptional 4-tuples (n, 2, 2, s) [64] and no exceptional 4-tuples (n, d, k, s) for large n (with some explicit bound)[1].”