论文标题
来自循环曲线的Weierstrass半群
Weierstrass semigroups from cyclic covers of hyperelliptic curves
论文作者
论文摘要
在平滑的代数曲线$ c $的点$ p $中，meromorthic函数的杆订单的{\ it weierstrass semigroup}是一个经典的研究对象； Hurwitz的一个著名问题是表征哪些半群$ {\ rm s} \ subset \ mathbb {n} $具有有限补体的{\ it realizable}是WeierStrass semigroups $ {\ rm s} = {\ rm s} = {\ rm s}（\ rm s}（c，c，p）$。在本说明中，我们建立了循环覆盖$π的可靠性结果：（c，p）\ rightarrow（b，q）$ b $ b $ b $ bug b $ bug b $ shipelliptic weierstrass点；我们表明，可实现性取决于$ j $折叠的行为在某些与我们的环状覆盖物自然相关的雅各布人中某些除数类别的乘法，因为$ j $范围在所有自然数字上。
The {\it Weierstrass semigroup} of pole orders of meromorphic functions in a point $p$ of a smooth algebraic curve $C$ is a classical object of study; a celebrated problem of Hurwitz is to characterize which semigroups ${\rm S} \subset \mathbb{N}$ with finite complement are {\it realizable} as Weierstrass semigroups ${\rm S}= {\rm S}(C,p)$. In this note, we establish realizability results for cyclic covers $π: (C,p) \rightarrow (B,q)$ of hyperelliptic targets $B$ marked in hyperelliptic Weierstrass points; and we show that realizability is dictated by the behavior under $j$-fold multiplication of certain divisor classes in hyperelliptic Jacobians naturally associated to our cyclic covers, as $j$ ranges over all natural numbers.
