论文标题
在高纤维曲线的模量空间的Kodaira尺寸上
On the Kodaira dimension of the moduli space of hyperelliptic curves with marked points
论文作者
论文摘要
众所周知，Moduli Space $ \ Overline {\ Mathcal {h}} _ {g，n} $属$ g $ stable的高纤维曲线，带有$ n $标记点的点是$ n \ leq 4g+5 $的$ n $标记点。在本文中，我们考虑互补案例。我们计算$ \ overline {\ Mathcal {h}} _ {g，n} $的规范除数，并表明它对$ n = 4g+6 $有效，对于$ n \ leq 4g+7 $。这使我们猜想$ \ edline {\ mathcal {h}} _ {g，n} $具有非负kodaira dimension $ n = 4g+6 $，并且是$ n \ geq 4g+7 $的常规类型。
It is known that the moduli space $\overline{\mathcal{H}}_{g,n}$ of genus $g$ stable hyperelliptic curves with $n$ marked points is uniruled for $n \leq 4g+5$. In this paper we consider the complementary case. We calculate the canonical divisor of $\overline{\mathcal{H}}_{g,n}$ and show that it is effective for $n=4g+6$ and big for $n\leq 4g+7$. This leads us to conjecture that $\overline{\mathcal{H}}_{g,n}$ has non-negative Kodaira dimension for $n = 4g+6$ and is of general type for $n \geq 4g+7$.
