Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Sur les vari\'et\'es X dans P^N telles que par n points passe une courbe
  de X de degr\'e donn\'e   Given integers r>1, n>1 and q> n-2, we consider projective varieties X of
dimension r+1 such that through n generic points of X passes a rational curve
of degree q, contained in X. More precisely, we study the class X_{r+1,n}(q) of
such varieties which moreover generate a projective space of the maximal
dimension.
  We determine all varieties of a class X_{r+1,n}(q) when q is not equal to
2n-3. In particuliar, we show that there exists a variety X' in P^{r+n-1}, of
minimal degree and a birational map F: X'---> X which sends a generic section
of X' by a P^{n-1} onto a rational normal curve of degree q.
  Without hypothesis on q, we define a quasi-grassmannian structure on the
space of the rational normal curves of degree q contained in a variety X of the
class X_{r+1,n}(q). We prove that X is of the form described above if and only
if this quasi-grassmannian structure is flat.
  We also give examples of varieties of the classes X_{r+1,3}(3) et
X_{r+1,4}(5) which are not of this form.

8
The categories of this paper are: hep-ex
21
The categories of this paper are: adap-org
24
The categories of this paper are: dg-ga
27
The categories of this paper are: comp-gas
11
The categories of this paper are: hep-lat
3
The categories of this paper are: physics
9
The categories of this paper are: nlin
33
The categories of this paper are: plasm-ph
14
The categories of this paper are: math-ph
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
23
The categories of this paper are: solv-int
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The categories of this paper are: hep-th
30
The categories of this paper are: q-alg
17
The categories of this paper are: q-fin
15
The categories of this paper are: nucl-ex