A note on Weierstrass points of bielliptic curves

Abstract

The family of all bielliptic curves of genus g greater than or equal to 6 can be divided into the subfamilies of all bielliptic curves of genus g with s Weierstrass points whose non-gap sequences are {4, 6, 8, ..., 2g - 4, 2g - 3, 2g - 2, 2g, 2g + 1, 2g + 2, ...}, where s = 0, 1, 2, ..., 2g - 2. We will prove that for any nonnegative integers g greater than or equal to 6, 0 less than or equal to s less than or equal to 2g - 2 and s not equal 2, 2g - 3, there exists a bielliptic curve of genus g with s Weierstrass points whose non-gap sequences are as above.