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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 difficult to do for
large genus. We introduce a natural generalization of the Wronskian matrix, which
depends on a sequence of integers s = m0,…,mg−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.
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