Weierstrass points with first two non-gaps equal to n and n+2

We study Weierstrass points on a smooth curve C whose first two nongaps are equal n and n + 2. If the genus g of C satisfies $g> [(n^2 -1)/2]$, then it is known that C is a two-sheeted covering of a curve. In this paper, we mainly concentrate on a point $P\in C$ such that $\vert nP \vert$ is a base point free pencil and $\vert (n + 2)P \vert$ is a bese point free simple net, whence necessarily $g \leq [(n^2 -1)/2]$, and study bounds for numbers of such Weierstrass points on $C$.

Publication year:2014

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Authors:International

Authors from:Higher Education

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