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The Speciality Lemma, Rank 2 Bundles and Gherardelli-type Theorems for Surfaces in P4

Published online by Cambridge University Press:  04 December 2007

Margherita Roggero  and
Paolo Valabrega
Margherita Roggero
Affiliation:
Dipartimento di Matematica dell' Università, Via Carlo Alberto 10, 10123 Turin, Italy. e-mail: margherita.roggero@unito.it
Paolo Valabrega
Affiliation:
Dipartimento di Matematica del Politecnico, Corso Duca degli Abruzzi 24, 10129 Turin, Italy. e-mail: paolo.valabrega@polito.it
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Abstract

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In the present paper we give a very short and easy proof of the speciality lemma for codimension 2 subvarieties, even those that are reducible or non-reduced, in Pn. Furthermore we give cohomological conditions that force a subcanonical surface in P4 to be a complete intersection and a rank 2 bundle to split, which generalize the classical First Theorem of Gherardelli.

Keywords

Gherardelli theoremsrank 2 bundlesspeciality lemmasubcanonical surfaces
Type
Research Article
Information
Compositio Mathematica , Volume 139 , Issue 1 , October 2003 , pp. 101 - 111
Copyright
© 2003 Kluwer Academic Publishers