The uniqueness of Weierstrass points with semigroup (cid:2) a ; b (cid:3) and related semigroups
The uniqueness of Weierstrass points with semigroup (cid:2) a ; b (cid:3) and related semigroups
复制标题
Weierstrass 点与半群 (cid:2) a 的唯一性；
DOI：
--
复制
发表时间：
2019
期刊：
影响因子：
--
通讯作者：
M. Coppens
中科院分区：
文献类型：
--
作者：
M. Coppens
假设a和b=na+r，其中n≥1和0<；r<；a是相对素数。如果C是光滑曲线，P是C上的一个点，且魏尔斯特拉斯半群等于<；a；b>；，则C称为Ca；b-曲线。在r(Cid：3)=a−1和b(Cid：3)=a+1的情况下，我们证明了C没有其他点Q(Cid：3)=P具有等于<；a；b>；的weierstrass半群，在这种情况下我们说weierstrass半群至多出现一次。曲线Ca；b有亏格(a−1)(b−1)/2，并将结果推广到亏格g<；(a−1)(b−1)/2.我们得到了g的一个下界，使得所有包含<；a；b>；的亏格g的Weerstrass半群至多出现一次.
Assume a and b = na + r with n ≥ 1 and 0 < r < a are relatively prime integers. In case C is a smooth curve and P is a point on C with Weierstrass semigroup equal to < a ; b > then C is called a C a ; b -curve. In case r (cid:3)= a − 1 and b (cid:3)= a + 1 we prove C has no other point Q (cid:3)= P having Weierstrass semigroup equal to < a ; b > , in which case we say that the Weierstrass semigroup < a ; b > occurs at most once. The curve C a ; b has genus ( a − 1 )( b − 1 )/ 2 and the result is generalized to genus g < ( a − 1 )( b − 1 )/ 2. We obtain a lower bound on g (sharp in many cases) such that all Weierstrass semigroups of genus g containing < a ; b > occur at most once.