论文标题
晶格多边形的模量尺寸
Moduli dimensions of lattice polygons
论文作者
论文摘要
鉴于带有$ g $内部晶格点的晶格多边形$ p $，我们将其与牛顿polygon $ p $的热带曲线曲线的模量相关联。我们完全对模量空间可以拥有的可能维度进行了分类。对于非hyperelliptic多边形，尺寸必须在$ g $至$ 2g+1 $之间，并且可以在此范围内承担任何整数值，仅在属属$ 3 $，$ 4 $和$ 7 $的情况下进行例外。我们为高纤维化多边形提供了类似的结果，其尺寸范围从$ g $到$ 2G-1 $。在非hyperelliptic多边形的情况下，我们的结果也适用于代数曲线的模量空间，而代数曲线相对于$ p $是非分类的。
Given a lattice polygon $P$ with $g$ interior lattice points, we associate to it the moduli space of tropical curves of genus $g$ with Newton polygon $P$. We completely classify the possible dimensions such a moduli space can have. For non-hyperelliptic polygons the dimension must be between $g$ and $2g+1$, and can take on any integer value in this range, with exceptions only in the cases of genus $3$, $4$, and $7$. We provide a similar result for hyperelliptic polygons, for which the range of dimensions is from $g$ to $2g-1$. In the case of non-hyperelliptic polygons, our results also hold for the moduli space of algebraic curves that are non-degenerate with respect to $P$.
