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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Authors define very nice and modest algebras axiomatically to link Hilbert-Samuel polynomials with multiplicity, generalize prior results from Ore domains to prime algebras, and establish the property for rational Cherednik algebras.
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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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Hilbert-Samuel Polynomials for Algebras with Special Filtrations
Authors define very nice and modest algebras axiomatically to link Hilbert-Samuel polynomials with multiplicity, generalize prior results from Ore domains to prime algebras, and establish the property for rational Cherednik algebras.