Abstract
We give a new method of constructing a non-Weierstrass semigroup H, which means that there is no smooth projective pointed curve over an algebracally closed field of characteristic 0 whose Weierstrass semigroup is H. This method depends on a description of a pointed smooth projective curve such that there exists a double covering of the curve ramified over the point with a certain condition on the genus of the covering curve. Using this we find non-Weierstrass semigroups whose minimum positive integers are 8 and 12, respectively.
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