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- Title
SECANTS TO THE VARIETY OF COMPLETELY REDUCIBLE FORMS AND THE HILBERT FUNCTION OF THE UNION OF STAR-CONFIGURATIONS.
- Authors
SHIN, YONG SU
- Abstract
We prove that if 핏 ≔ 핏(t, s) is the union of two linear star-configurations of type t × s for 3 ≤ t ≤ 9 and s ≥ t in ℙ2, then 핏 has generic Hilbert function. We also show that (I핏)s = {0} when 핏 is the union of two linear star-configurations of type s × s for s ≥ 6. Moreover, using the two results with the work in [E. Arrondo and A. Bernardi, On the variety parameterizing completely decomposable polynomials, J. Pure Appl. Algebra 215(3) (2011) 201-220], we prove that the secant variety 1(s(ℙn)) is not defective for s ≥ 3 and n ≥ 2.
- Subjects
MATHEMATICAL forms; HILBERT functions; POLYNOMIALS; MATHEMATICAL decomposition; LINEAR systems; MATHEMATICAL proofs
- Publication
Journal of Algebra & Its Applications, 2012, Vol 11, Issue 6, p-1
- ISSN
0219-4988
- Publication type
Article
- DOI
10.1142/S0219498812501095