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Ideals of varieties parameterized by certain symmetric tensors

Alessandra Bernardi 1 
1 GALAAD - Geometry, algebra, algorithms
CRISAM - Inria Sophia Antipolis - Méditerranée , UNS - Université Nice Sophia Antipolis (1965 - 2019), CNRS - Centre National de la Recherche Scientifique : UMR6621
Abstract : The ideal of a Segre variety $\PP {n_{1}}\times \cdots \times \PP {n_{t}}\hookrightarrow \PP {(n_{1}+1)\cdots (n_{t}+1)-1}$ is generated by the $2$-minors of a generic hypermatrix of indeterminates (see \cite{Ha1} and \cite{Gr}). We extend this result to the case of Segre-Veronese varieties. The main tool is the concept of ''weak generic hypermatrix'' which allows us to treat also the case of projection of Veronese surfaces from a set of general points and of Veronese varieties from a Cohen-Macaulay subvariety of codimension $2$.
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Submitted on : Monday, November 28, 2011 - 10:32:04 PM
Last modification on : Wednesday, September 14, 2022 - 5:14:26 PM
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Alessandra Bernardi. Ideals of varieties parameterized by certain symmetric tensors. Journal of Pure and Applied Algebra, 2008, 212 (6), pp.1542-1559. ⟨10.1016/j.jpaa.2007.10.022⟩. ⟨hal-00645965⟩

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