Abstract
AbstractIn this paper we prove that if $$X\subset {\mathbb P}^r$$
X
⊂
P
r
is a 2-smooth, irreducible, projective non-degenerate variety of dimension n such that $${\text {Sec}}_2(X)={\mathbb P}^r$$
Sec
2
(
X
)
=
P
r
, if $$n > \frac{4}{7}(r-2)$$
n
>
4
7
(
r
-
2
)
and if $$X'$$
X
′
is the projection of X to $${\mathbb P}^{r-1}$$
P
r
-
1
from a general point, then the set of length 3 subschemes of $$X'$$
X
′
which lie on a line form an irreducible variety.
Funder
Università degli Studi di Roma Tor Vergata
Publisher
Springer Science and Business Media LLC
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