WEIERSTRASS POINTS WITH FIRST TWO NON-GAPS EQUAL TO n AND n + 2

摘要

We study Weierstrass points on a smooth curve C whose first two non-gaps equal n and n + 2. If the genus g of C satisfies g > [(n2 ? 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 ∈ C such that |nP | is a base point free pencil and |(n + 2)P | is a base point free simple net, whence necessarily g ≤ [(n2 ? 1)/2], and study bounds for numbers of suchWeierstrass points on C.