论文标题
在其模量空间的特殊层中的属-3曲线的还原类型
Reduction type of genus-3 curves in a special stratum of their moduli space
论文作者
论文摘要
我们研究一个3维层$ \ MATHCAL {M} _ {3，V} $的Moduli Space $ \ MathCal {M} _3 c曲线的曲线$ 3 $ 3 $参数化曲线$ y $，该曲线承认某些$ v = c_2 f = c_2 fips times c_2 \ \ times c_2 $。我们确定将这些曲线稳定减少到特征与$ 2 $不同的可能类型。我们为$ \ Mathcal {M} _ {3，V} $定义不变性，并以它们的方式表征每种减少类型的出现。我们还计算了$ j $ invariant（分别是igusa不变的），这是不变的稳定减少$ y $的不可约组成部分的不变属。
We study a 3-dimensional stratum $\mathcal{M}_{3,V}$ of the moduli space $\mathcal{M}_3$ of curves of genus $3$ parameterizing curves $Y$ that admit a certain action of $V= C_2\times C_2$. We determine the possible types of the stable reduction of these curves to characteristic different from $2$. We define invariants for $\mathcal{M}_{3,V}$ and characterize the occurrence of each of the reduction types in terms of them. We also calculate the $j$-invariant (resp. the Igusa invariants) of the irreducible components of positive genus of the stable reduction of $Y$ in terms of the invariants.
