| Abstrakt: |
Let | L g | , be the genus g du Val linear system on a Halphen surface Y of index k. We prove that the Clifford index Cliff (C) is constant on smooth curves C ∈ | L g | . Let γ (C) be the gonality of C. When Cliff (C) < ⌊ g - 1 2 ⌋ (the relevant case), we show that γ (C) = Cliff (C) + 2 = k , and that the gonality is realized by the Weierstrass linear series | - k K Y | C | , which is totally ramified at one point. The proof of the first statement follows closely the path indicated by Green and Lazarsfeld for a similar statement regarding K3 surfaces. [ABSTRACT FROM AUTHOR] |
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