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On the number of moduli of extendable canonical curves

Published online by Cambridge University Press:  22 January 2016

Ciro Ciliberto  and
Angelo Felice Lopez
Ciro Ciliberto
Affiliation:
Dipartimento di Matematica Universitè di Roma “Tor Vergata”, Viale della Ricerca Scientifica 00133 Roma, Italy, [email protected]
Angelo Felice Lopez
Affiliation:
Dipartimento di Matematica Universitè di Roma Tre, Largo San Leonardo Murialdo 1 00146 Roma, Italy, [email protected]
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Abstract

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Let C ⊂ ℙg−1 be a canonical curve of genus g. In this article we study the problem of extendability of C, that is when there is a surface S ⊂ ℙg different from a cone and having C as hyperplane section. Using the work of Epema we give a bound on the number of moduli of extendable canonical curves. This for example implies that a family of large dimension of curves that are cover of another curve has general member nonextendable. Using a theorem of Wahl we prove the surjectivity of the Wahl map for the general k-gonal curve of genus g when k = 5, g ≥ 15 or k = 6, g ≥ 13 or k ≥ 7, g ≥ 12.

Keywords

14H1014J1014J26
Type
Research Article
Information
Nagoya Mathematical Journal , Volume 167 , 2002 , pp. 101 - 115
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 2002

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