Quasi-symmetric numerical semigroups on triple covers of curves (Logic, Language, Algebraic system and Related Areas in Computer Science)

This paper is an extended abstract and the details were published (see [J. Komeda, A classification of the quasi-symmetric numerical semigroups through their division by 3, In preparation.])We study quasi-symmetric numerical semigroups through the map dividing by 3. We give quasi-symmetric numerical semigroups which are the Weierstrass semigroups of ramification points of triple cyclic covers of the projective line. Moreover, we find examples of quasi-symmetric Weierstrass numerical semigroups which cannot be attained by any ramification point of a triple cyclic cover of the projective line. We also construct many quasi-symmetric non-Weierstrass numerical semigroups