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Journal of the London Mathematical Society Advance Access published online on May 4, 2009
Journal of the London Mathematical Society, doi:10.1112/jlms/jdp004
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© 2009 London Mathematical Society

On rational normal curves in projective space

E. Carlini

Dipartimento di Matematica
Politecnico di Torino
Corso Duca degli Abruzzi 24
10129 Turin
Italy

M. V. Catalisano

DIPTEM – Dipartimento di Ingegneria della Produzione
Termoenergetica e Modelli Matematici
Università degli Studi di Genova
Piazzale Kennedy
pad. D 16129 Genoa
Italy
catalisano@diptem.unige.it

In this article we consider a generalization of a well-known result by Veronese about rational normal curves. More precisely, given a collection of linear spaces in Pn, we study the existence of rational normal curves intersecting each component of the configuration maximally. We introduce different methods to show the existence and non-existence of such curves. We also show how to apply these techniques to the study of defectivity of Segre–Veronese varieties.

2000 Mathematics Subject Classification 14H45; 14N20.

Received May 23, 2008; revised December 9, 2008;
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