Abstract: Let be a non-hyperelliptic curve of genus . We recall some facts about curves endowed with a base-point-free . Then we prove that if the minimal degree of a surface containing the canonical model of in is , then and carries exactly one . As a by-product, we deduce that if the canonical model of in is contained in a surface of degree at most , then is either trigonal or tetragonal or isomorphic to a plane sextic.
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G. Casnati Affiliation:
Dipartimento di Matematica, Politecnico di Torino, c.so Duca degli Abruzzi 24, 10129 Torino, Italy
Email:
casnati@calvino.polito.it