SECANTS TO THE VARIETY OF COMPLETELY REDUCIBLE FORMS AND THE HILBERT FUNCTION OF THE UNION OF STAR-CONFIGURATIONS

DOI10.1142/S0219498812501095zbMath1263.13013MaRDI QIDQ3144375

Yong Su Shin

Publication date: 7 December 2012

Published in: Journal of Algebra and Its Applications (Search for Journal in Brave)

zbMATH Keywords

secant varietiesstar configurationsplit Varietiesvarieties of decomposable forms

Mathematics Subject Classification ID

Hilbert-Samuel and Hilbert-Kunz functions; Poincaré series (13D40) Complete intersections (14M10) Projective techniques in algebraic geometry (14N05)

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Cites Work

• Combinatorial bounds on Hilbert functions of fat points in projective space
• On the variety parameterizing completely decomposable polynomials
• Complete intersections on general hypersurfaces
• On Waring's problem for several algebraic forms
• On the ideals of secant varieties of Segre varieties
• On the first infinitesimal neighborhood of a linear configuration of points in \(\mathbb P^2\)
• Secant varieties of ℙ¹×⋯×ℙ¹ (𝕟-times) are NOT defective for 𝕟≥5
• Star configuration points and generic plane curves
• Comparing powers and symbolic powers of ideals
• Induction for secant varieties of Segre varieties
• Secant varieties of Grassmann varieties