منابع مشابه
On the third secant variety
We determine normal forms and ranks of tensors of border rank at most three. We present a differential-geometric analysis of limits of secant planes in a more general context. In particular there are at most four types of points on limiting trisecant planes for cominuscule varieties such as Grassmannians. We also show that the singular locus of the secant varieties σr(Seg(P × P × P)) has codime...
متن کاملON THE CONCEPT OF k-SECANT ORDER OF A VARIETY
For a variety X of dimension n in Pr, r n(k + 1) + k, the kth secant order of X is the number μk(X) of (k + 1)-secant k-spaces passing through a general point of the kth secant variety. We show that, if r > n(k + 1) + k, then μk(X) = 1 unless X is k-weakly defective. Furthermore we give a complete classification of surfaces X ⊂ Pr, r > 3k + 2, for which μk(X) > 1.
متن کاملSyzygies of the Secant Variety of a Curve
We show the secant variety of a linearly normal smooth curve of degree at least 2g + 3 is arithmetically Cohen-Macaulay, and we use this information to study the graded Betti numbers of the secant variety.
متن کاملGeneration and Syzygies of the First Secant Variety
We show that the secant variety to a smooth variety embedded by a sufficiently positive line bundle satisfies N3,p. For smooth curves, we find the effective bound of degree at least max ̆ 3g + 3 + p, 1 2 (7g + 4 + p) ̄
متن کاملRegularity of the Secant Variety to a Projective Curve
We give a sharp bound on the regularity of the secant variety to a smooth curve embedded by a line bundle of large (effective) degree.
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ژورنال
عنوان ژورنال: Journal of Algebraic Combinatorics
سال: 2014
ISSN: 0925-9899,1572-9192
DOI: 10.1007/s10801-013-0495-0