The Rough Veronese variety
نویسندگان
چکیده
منابع مشابه
A Dimension Formula for the Nucleus of a Veronese Variety∗
The nucleus of a Veronese variety is the intersection of all its osculating hyperplanes. Various authors have given necessary and sufficient conditions for the nucleus to be empty. We present an explicit formula for the dimension of this nucleus for arbitrary characteristic of the ground field. As a corollary, we obtain a dimension formula for that subspace in the t–th symmetric power of a fini...
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If X ⊂ Pn is a projective non degenerate variety, the X-rank of a point P ∈ Pn is defined to be the minimum integer r such that P belongs to the span of r points of X. We describe the complete stratification of the fourth secant variety of any Veronese variety X via the X-rank. This result has an equivalent translation in terms both of symmetric tensors and homogeneous polynomials. It allows to...
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In this paper we prove that the coordinate ring of the pinched Veronese (i.e k[X, XY, XY , Y , XZ, Y Z, XZ, Y Z, Z] ⊂ k[X, Y, Z]) is Koszul. The strategy of the proof is the following: we can consider a presentation S/I where S = k[X1, . . . , X9]. Using a distinguished weight ω, it’s enough to show that S/inωI is Koszul. We write inωI as J + H where J is generated by a Gröbner basis of quadric...
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A conic of the Veronese surface in PG(5, 3) is a quadrangle. If one such quadrangle is replaced with its diagonal triangle, then one obtains a point model K for Witt’s 5–(12, 6, 1) design, the blocks being the hyperplane sections containing more than three (actually six) points of K. As such a point model is projectively unique, the present construction yields an easy coordinate–free approach t...
متن کاملDegenerations of the Veronese and Applications
The classical Hermite interpolation technique approximates a given differentiable function defined in an open subset of R with a polynomial of a given degree which takes at an assigned set points p1, . . . , pn, usually assumed to be sufficiently general, the same values as the function and of its derivatives up to orderm1, . . . ,mn respectively. A geometric counterpart of Hermite interpolatio...
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ژورنال
عنوان ژورنال: Linear Algebra and its Applications
سال: 2019
ISSN: 0024-3795
DOI: 10.1016/j.laa.2019.08.029