Abstract

Given a point P on a smooth projective curve C of genus g, one can determine the Weierstrass weight of that point by looking at a certain Wronskian. In practice, this computation is dificult to do for large genus. We introduce a natural generalization of the Wronskian matrix, which depends on a sequence of integers s = m₀,…,m_g−1 and show that the determinant of our matrix is nonzero at P if and only if s is the non-gap sequence at P.

As an application, we compute the weights of certain points on the F₉ and F₁₀, the 9th and 10th Fermat curves. These weights correspond to the expected weights predicted in an earlier paper.