Jiryo Komeda

On the existence of Weierstrass gap sequences on curves of genus ≤8

We show that for any possible Weierstrass non-gap sequence H on a curve of genus ≤7 (resp. genus 8 with twice the smallest positive non-gap > the largest gap) there exist a pointed curve (C,P) such that the non-gap sequence at P is H.

On the existence of Weierstrass points whose first non-gaps are five

LetH be a numerical semigroup, i.e., a subsemigroup of the additive semigroup N of non-negative integers whose complement N/H in N is finite. Leta be the least positive integer inH. Then we show that ifa=5, then there exists a pointed complete non-singular irreducible algebraic curve (C, P) such thatH is the set of integers which are pole orders atP of regular functions onC/{P}.

Weierstrass Semigroups of a Pair of Points Whose First Nongaps are Three

We found all candidates for a Weierstrass semigroup at a pair of Weierstrass points whose first nongaps are three. We prove that such semigroups are actually Weierstrass semigroups by constructing examples.

The Weierstrass semigroup of a pair and moduli inM3

We classify all the Weierstrass semigroups of a pair of points on a curve of genus 3, by using its canonical model in the plane. Moreover, we count the dimension of the moduli of curves which have a pair of points with a specified Weierstrass semigroup.

Double Coverings of Curves and Non-Weierstrass Semigroups

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.

The Riemann constant for a non-symmetric Weierstrass semigroup

AbstractThe zero divisor of the theta function of a compact Riemann surface X of genus g is the canonical theta divisor of Pic

Non-Weierstrass Numerical Semigroups

{^{(g-1)}}

On primitive Schubert indices of genus g and weight g-1

(g-1) up to translation by the Riemann constant