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Journal of the London Mathematical Society Advance Access published online on August 17, 2007
Journal of the London Mathematical Society, doi:10.1112/jlms/jdm042
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© 2007 London Mathematical Society

Existence results for rational normal curves

E. Carlini

Dipartimento di Matematica
Politecnico di Torino
C.so Duca degli Abruzzi, 24
10129 Torino
Italy enrico.carlini{at}polito.it

M. V. Catalisano

DIPTEM
Università di Genova
P. le Kennedy Pad. D
16129 Genova
Italy

In this paper we study existence of rational normal curves in Pn passing through p points and intersecting l codimension-two linear spaces in n – 1 points each. If p + l = n + 3 and the points and the linear spaces are general, then one expects the curve to exist, but this is not always the case. For p > 0, our main result precisely describes in which cases the curve exists and in which it does not exist. Moreover, when there is existence we also show that the curve is unique.

catalisano{at}diptem.unige.it

2000 Mathematics Subject Classification 14H50, 14C15.

Received March 3, 2006; revised September 27, 2006;
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