论文标题
铅笔在正常交叉处的表面和$ \叠加的kodaira尺寸{\ mathcal {m}} _ {g，n} $
Pencils on surfaces with normal crossings and the Kodaira dimension of $\overline{\mathcal{M}}_{g,n}$
论文作者
论文摘要
我们研究曲线铅笔在正常交叉处的平滑。结果，我们表明$ \ overline {\ mathcal {m}} _ {g，n} $的规范除数在某些范围内不是伪有效的，这意味着$ \ OVERLINE {\ MATHCAL {M}} _ {12,6}，\ overline {\ MathCal {M}} _ {12,7}，\ edrowlline {\ Mathcal {M Mathcal {M}} _未释放。我们为$ \ overline {\ Mathcal {m}} _ {12,8} $和$ \ overline {\ Mathcal {M}} _ {16} $的Kodaira维度提供上限。我们还表明，$（4G+5）$ - 指向的高纤维曲线的模量$ \ MATHCAL {H} _ {G，4G+5} $是未释放的。加上施瓦茨的最新结果，这是尖曲线模量的Kodaira分类。
We study smoothing of pencils of curves on surfaces with normal crossings. As a consequence we show that the canonical divisor of $\overline{\mathcal{M}}_{g,n}$ is not pseudo-effective in some range, implying that $\overline{\mathcal{M}}_{12,6},\overline{\mathcal{M}}_{12,7},\overline{\mathcal{M}}_{13,4}$ and $\overline{\mathcal{M}}_{14,3}$ are uniruled. We provide upper bounds for the Kodaira dimension of $\overline{\mathcal{M}}_{12,8}$ and $\overline{\mathcal{M}}_{16}$. We also show that the moduli of $(4g+5)$-pointed hyperelliptic curves $\mathcal{H}_{g,4g+5}$ is uniruled. Together with a recent result of Schwarz, this concludes the Kodaira classification for moduli of pointed hyperelliptic curves.
