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Projective surfaces with K-very ample line bundles of degree ≤ 4K + 4

Published online by Cambridge University Press:  22 January 2016

Edoardo Ballico  and
Andrew J. Sommese
Edoardo Ballico
Affiliation:
Dipartimento di Matematica, Università di Trento, 38050 Povo (TN), Italia, ballico@itncisca.bitnet, fax: Italy +461881624
Andrew J. Sommese
Affiliation:
Department of Mathematics, University of Notre Dame, Notre Dame, Indiana 46556, U.S.A., sommese.1@nd.edu, fax: U.S.A. +219-631-6579
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A line bundle, L, on a smooth, connected projective surface, S, is defined [7] to be k-very ample for a non-negative integer, k, if given any 0-dimensional sub-scheme with length , it follows that the restriction map is onto. L is 1-very ample (respectively 0-very ample) if and only if L is very ample (respectively spanned at all points by global sections). For a smooth surface, S, embedded in projective space by | L | where L is very ample, L being k-very ample is equivalent to there being no k-secant Pk−1 to S containing ≥ k + 1 points of S.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 136 , December 1994 , pp. 57 - 79
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1994

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