The authors define divisible weighted projective spaces, give sharp bounds for minimal-degree non-degenerate subvarieties therein, and develop a theory of weighted determinantal scrolls that achieve minimal degree while satisfying weighted N_p properties tied to regularity notions.
Symmetric tensor decomposition , volume =
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Establishes equivalence between Hankel flat extension and multiplication tensor completion for cactus rank in Artinian Gorenstein algebras, plus reduction of basis shapes via Borel-fixed staircases.
Gives explicit characterization and algorithm for Waring decompositions of symmetric tensors on rational varieties under a technical assumption, generalizing Hankel tensors, plus new quadrature bounds on rational curves.
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Varieties of minimal degree in weighted projective space
The authors define divisible weighted projective spaces, give sharp bounds for minimal-degree non-degenerate subvarieties therein, and develop a theory of weighted determinantal scrolls that achieve minimal degree while satisfying weighted N_p properties tied to regularity notions.
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Hankel and Multiplication Tensor Completions for Cactus Rank
Establishes equivalence between Hankel flat extension and multiplication tensor completion for cactus rank in Artinian Gorenstein algebras, plus reduction of basis shapes via Borel-fixed staircases.
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Symmetric tensor decomposition on rational varieties
Gives explicit characterization and algorithm for Waring decompositions of symmetric tensors on rational varieties under a technical assumption, generalizing Hankel tensors, plus new quadrature bounds on rational curves.