Academic literature on the topic 'Apolarity Theory'

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Journal articles on the topic "Apolarity Theory"

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Ballico, E., G. Casnati, and R. Notari. "Canonical curves with low apolarity." Journal of Algebra 332, no. 1 (2011): 229–43. http://dx.doi.org/10.1016/j.jalgebra.2010.12.030.

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Ehrenborg, Richard. "On Apolarity and Generic Canonical Forms." Journal of Algebra 213, no. 1 (1999): 167–94. http://dx.doi.org/10.1006/jabr.1995.6649.

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3

Morikawa, Hisasi. "On differential polynomials, II." Nagoya Mathematical Journal 148 (December 1997): 73–112. http://dx.doi.org/10.1017/s0027763000006449.

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AbstractIn Part II, we shall be concerned with applications of classical invariant theory, to statistic physics and to theta functions. Main theorem in Chapter 2 is stated as follows:For a partition functionsatisfying γl ≥ 0 (l ≥ 1) and α > 0, the 2n-apolar of ξ(s)has the expansionsuch that βn,1 ≥ 0 (l ≥ 2). This means, for a given partition function ξ(s) with nonnegative relative probabilities, we construct a sequence of partition functions A2n (ξ(s), ξ(s))n≥1 with the same properties, which may be considered a sequence of symbolical higher derivative of ξ(s). The main theorem in Chapter 3
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4

Staffolani, Reynaldo. "Schur apolarity." Journal of Symbolic Computation, April 2022. http://dx.doi.org/10.1016/j.jsc.2022.04.017.

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Dissertations / Theses on the topic "Apolarity Theory"

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Staffolani, Reynaldo. "Schur apolarity and how to use it." Doctoral thesis, Università degli studi di Trento, 2022. https://hdl.handle.net/11572/330432.

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The aim of this thesis is to investigate the tensor decomposition of structured tensors related to SL(n)-irreducible representations. Structured tensors are multilinear objects satisfying specific symmetry relations and their decompositions are of great interest in the applications. In this thesis we look for the decompositions of tensors belonging to irreducible representations of SL(n) into sum of elementary objects associated to points of SL(n)-rational hoogeneous varieties. This family includes Veronese varieties (symmetric tensors), Grassmann varieties (skew-symmetric tensors), and flag v
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Jelisiejew, Joachim. "Hilbert schemes of points and their applications." Doctoral thesis, 2017. https://depotuw.ceon.pl/handle/item/2235.

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This thesis is concerned with deformation theory of finite subschemes of smooth varieties. Of central interest are the smoothable subschemes (i.e., limits of smooth subschemes). We prove that all Gorenstein subschemes of degree up to 13 are smoothable. This result has immediate applications to finding equations of secant varieties.We also give a description of nonsmoothable Gorenstein subschemes of degree 14, together with an explicit condition for smoothability.We prove that being smoothable is a local property, that it does not depend on the embedding and it is invariant under a base field
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