Normal bundle of rational curves and Waring decomposition
نویسندگان
چکیده
منابع مشابه
Nuclei of Normal Rational Curves
A k–nucleus of a normal rational curve in PG(n, F ) is the intersection over all k–dimensional osculating subspaces of the curve (k ∈ {−1, 0, . . . , n− 1}). It is well known that for characteristic zero all nuclei are empty. In case of characteristic p > 0 and #F ≥ n the number of non–zero digits in the representation of n+ 1 in base p equals the number of distinct nuclei. An explicit formula ...
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The completeness of normal rational curves, considered as (q + 1)-arcs in PG(n, q), is investigated. Previous results of Storme and Thas are improved by using a result by Kovacs. This solves the problem completely for large prime numbers q and odd nonsquare prime powers q = p2h+l with p prime, p > po(h), h>\,1where po(h) is an odd prime number which depends on h.
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We construct dynamical systems with Pn as state space, using (n+1)×(n+1) matrices of linear forms in n+1 variables, such that the fixed point sets are rational normal curves minus one point. Our matrices provide canonical forms for the triple action of PGLn+1 on the projective space of such matrices. Our dynamical systems include parameters identified with points in Pn−1. We find conditions on ...
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Each normal rational curve Γ in PG(n, F ) admits a group PΓL(Γ) of automorphic collineations. It is well known that for characteristic zero only the empty and the entire subspace are PΓL(Γ)–invariant. In case of characteristic p > 0 there may be further invariant subspaces. For #F ≥ n+ 2, we give a construction of all PΓL(Γ)–invariant subspaces. It turns out that the corresponding lattice is to...
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in this note we consider smooth rational curves C of degree n in threedimensional projective space IP 3 (over a closed field of characteristic 0). To avoid trivial exceptions we shall always assume that n ~ 4 (this does not hold however for certain auxiliary curves we shall consider). Let N = N c be the normal bundle of C in IP 3. Since degel(IP3)=4, and d e g c l ( l P 0 = 2 , we have that d e...
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 2014
ISSN: 0021-8693
DOI: 10.1016/j.jalgebra.2013.11.008