The Weierstrass semigroups on double covers of genus two curves

We show that three numerical semigroups , and are of double covering type, i.e., the Weierstrass semigroups of ramification points on double covers of curves. Combining this with the results of Oliveira-Pimentel and Komeda we can determine the Weierstrass semigroups of the ramification points on double covers of genus two curves.Comment: 5 page

First order deformations of cones over projectively normal hyperelliptic curves

Let X be a smooth, proper algebraic variety over an algebraically ciosea field k, and let L be an ample, priojectively normal invertible sheaf in X. ..