Number of weak Galois-Weierstrass points with Weierstrass semigroups generated by two elements
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Let $C$ be a nonsingular projective curve of genus $\geq 2$ over an algebraically closed field of characteristic $0$. For a point $P$ in $C$, the Weierstrass semigroup $H(P)$ is defined as the set of non-negative integers $n$ for which there exists a rational function $f$ on $C$ such that the order of the pole of $f$ at $P$ is equal to $n$, and $f$ is regular away from $P$. A point $P$ in $C$ is referred to as a weak Galois-Weierstrass point if $P$ is a Weierstrass point and there exists a Galois morphism $\varphi : C \rightarrow \mathbb{P}^1$ such that $P$ is a total ramification point of $\varphi$. In this paper, we investigate the number of weak Galois-Weierstrass points of which the Weierstrass semigroups are generated by two positive integers.
Abstract
Let $C$ be a nonsingular projective curve of genus $\geq 2$ over an algebraically closed field of characteristic $0$. For a point $P$ in $C$, the Weierstrass semigroup $H(P)$ is defined as the set of non-negative integers $n$ for which there exists a rational function $f$ on $C$ such that the order of the pole of $f$ at $P$ is equal to $n$, and $f$ is regular away from $P$. A point $P$ in $C$ is referred to as a weak Galois-Weierstrass point if $P$ is a Weierstrass point and there exists a Galois morphism $\varphi : C \rightarrow \mathbb{P}^1$ such that $P$ is a total ramification point of $\varphi$. In this paper, we investigate the number of weak Galois-Weierstrass points of which the Weierstrass semigroups are generated by two positive integers.
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