Non-secant defectivity via osculating projections
نویسندگان
چکیده
منابع مشابه
Osculating spaces to secant varieties
We generalize the classical Terracini’s Lemma to higher order osculating spaces to secant varieties. As an application, we address with the so-called Horace method the case of the d-Veronese embedding of the projective 3-space. A.M.S. Math. Subject Classification (2000): 14N05.
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Fix integers s ≥ 2 and n ≥ 1. Set x̃i := n + i − 1 if 3 ≤ i ≤ s and x̃2 := max{3, n+ 1}. Set x̃1 := 9 if n = 1 and x̃1 = n!(n+ 1)− n if n ≥ 2. Fix integers xi ≥ x̃i, 1 ≤ i ≤ s. Here we prove that the line bundle OPn×(P1)s−1(x1, . . . , xs) is not weakly defective, i.e. for every integer z such that z(n + s) + 1 ≤ ( n+x1 n ) ∏ s i=2(xi + 1) the linear system |IZ(x1, . . . , xs)| has dimension ( n+x1 ...
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ژورنال
عنوان ژورنال: ANNALI SCUOLA NORMALE SUPERIORE - CLASSE DI SCIENZE
سال: 2019
ISSN: 2036-2145,0391-173X
DOI: 10.2422/2036-2145.201611_012