Higher order Weierstrass points on genus two curves

The study of q-Weierstrass points on a compact Riemann surface is a fascinating topic, rich in geometrical applications and still a ?flourishing area of research. Around 1893, Hurwitz introduced the space of q-differential as the space of forms of order q on the space of holomorphic differential on a compact Riemann surface. He was led to the concept of what we now call Weierstrass points of order q, or higher order Weierstrass points. It is well known that, for a hyperelliptic curve the set of ordinary Weierstrass points are nothing but its set of the ramifi?cation points. In this book, we classify the 3-Weierstrass points on the genus two curves with two parameters. We describe the classification in terms of some invariants maps in its moduli space.