We calculate the Masur–Veech volume of the gothic locus $\mathcal{G}$ in the stratum $\mathcal{H}(2^3)$ of genus 4. Our method is based on the use of the formulae for the Euler characteristics of gothic Teichmüller curves to determine the number of lattice points of given area. We also use this method to recalculate the Masur–Veech volumes of the Prym loci ${\mathcal{P}}_3\subset \mathcal{H}(4)$ and ${\mathcal{P}}_4\subset \mathcal{H}(6)$ in genus 3 and 4.

中文翻译：

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哥特式场所的Masur-Veech体积

我们计算哥特式场所的Masur-Veech体积 $\mathcal{G}$ 在阶层中 $\mathcal{H}（2^3）$属4。我们的方法是基于使用哥特式Teichmüller曲线的Euler特性公式来确定给定区域的晶格点数。我们还使用此方法重新计算Prym位点的Masur-Veech体积${\mathcal{P}}_3\subset \mathcal{H}（4）$ 和 ${\mathcal{P}}_4\subset \mathcal{H}（6）$ 在属3和4。