JP Journal of Geometry and Topology
Volume 10, Issue 3, Pages 191 - 229
(November 2010)
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ON THE NUMBER OF PENCILS OF MINIMAL DEGREE ON CURVES WITH SMALL GONALITY
Takeshi Harui and Akira Ohbuchi
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Abstract:
A smooth curve of genus eight has only finitely many pencils of minimal degree unless it is bielliptic. This paper is devoted to determining possible numbers of such pencils for numerically special cases. In particular, it is shown that there exists a pentagonal curve of genus eight with a net of degree seven possessing exactly s pencils of degree five for any positive number s not greater than fourteen, the maximal possible number. |
| Keywords and phrases: gonality, pencil, affine equation. |
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