论文标题
Prym枚举几何形状和$ \ edline {\ Mathcal {r}} _ {2i} $中的hurwitz除数
Prym enumerative geometry and a Hurwitz divisor in $\overline{\mathcal{R}}_{2i}$
论文作者
论文摘要
对于$ i \ geq2 $，我们计算了Prym曲线模型的理性Picard组中的类$ [\ overline {d}（μ; 3）] $的第一个系数存在$ 2i $ map $π\ colon c \ rightarrow \ mathbb {p}^1 $具有分支化配置文件$ $（2，\ ldots，2）$上方两个点$ q_1 $ q_1，q_2 $，在其他地方进行三重分支，并令人满意$ \ MATHCAL {O} _C（\ frac {π^{*}（q_1）-π^{*}（q_2）} {2}）\ congη$。此外，我们还提供了与这种情况有关的几个新的列举结果。
For $i\geq2$, we compute the first coefficients of the class $[\overline{D}(μ;3)]$ in the rational Picard group of the moduli of Prym curves $\overline{\mathcal{R}}_{2i}$, where $D(μ;3)$ is the divisor parametrizing pairs $[C,η]$ for which there exists a degree $2i$ map $π\colon C\rightarrow \mathbb{P}^1$ having ramification profile $(2,\ldots,2)$ above two points $q_1, q_2$, a triple ramification somewhere else and satisfying $\mathcal{O}_C(\frac{π^{*}(q_1)-π^{*}(q_2)}{2})\cong η$. Furthermore, we provide several new Prym enumerative results related to this situation.
