极小层的自旋体积与Chiodo积分
Spin volumes of minimal strata and Chiodo integrals
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中文总结 AI 辅助
该研究推导了阿贝尔微分层自旋-宇称分量的Masur-Veech体积闭式公式，计算了相关虚拟体积的自旋对应物及特定Chiodo积分，为相关不变量的分量计算提供了方法。
中文摘要 AI 辅助
我们推导了具有单个最大阶零点的阿贝尔微分层的自旋-宇称分量的Masur-Veech体积的闭式公式。我们的方法基于Holmes-Politopoulos-Sauvaget近期发展的Hodge丛内部自旋-宇称平方的虚拟子锥的相交理论，这是Sauvaget经典结果的自旋改进，且与Chen-Möller-Sauvaget-Zagier的格点计数技术一致。我们进一步将该理论应用于计算Sauvaget近期定义的虚拟体积的自旋对应物，这些虚拟体积与面积Siegel-Veech常数相关，我们能够按分量计算这些不变量。此外，通过比较我们对非宇称平方的方法与Sauvaget的经典结果，我们计算了特定的Chiodo积分。
英文摘要
We derive a closed formula for the Masur-Veech volumes of spin-parity components of the stratum of abelian differentials with a single zero of maximal order. Our approach is based on the intersection theory of the virtual subcone of spin-parity squares inside the Hodge bundle, recently developed by Holmes-Politopoulos-Sauvaget. This is a spin refinement of a classical result of Sauvaget and agrees with the lattice-point counting technique of Chen-Möller-Sauvaget-Zagier. We further apply this theory to compute spin counterparts of virtual volumes, defined recently by Sauvaget. These virtual volumes are related to area Siegel-Veech constants and we are able to compute these invariants component-wise. In addition, by comparing our method for non-parity squares with the classical result of Sauvaget, we compute specific Chiodo integrals.
