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Explicit Noether–Lefschetz for arbitrary threefolds

Published online by Cambridge University Press:  01 September 2007

ANGELO FELICE LOPEZ  and
CATRIONA MACLEAN
ANGELO FELICE LOPEZ
Affiliation:
Dipartimento di Matematica, Università di Roma Tre, Largo San Leonardo Murialdo 1, 00146, Roma, Italy. email: lopez@mat.uniroma3.it
CATRIONA MACLEAN
Affiliation:
UFR de Mathèmatiques, UMR 5582 CNRS/Universitè J. Fourier 100, rue des Maths, BP 74, 38402 St Martin d'Heres, France. email: Catriona.MacLean@ujf-grenoble.fr
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Abstract

We study the Noether–Lefschetz locus of a very ample line bundle L on an arbitrary smooth threefold Y. Building on results of Green, Voisin and Otwinowska, we give explicit bounds, depending only on the Castelnuovo–Mumford regularity properties of L, on the codimension of the components of the Noether–Lefschetz locus of |L|.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 143 , Issue 2 , September 2007 , pp. 323 - 342
Copyright
Copyright © Cambridge Philosophical Society 2007

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