论文标题
一种计算差分层旋转成分基本类别的算法
An algorithm to compute fundamental classes of spin components of strata of differentials
论文作者
论文摘要
我们构建了一种用于计算稳定曲线模量空间$ \ overline {\ mathcal {m}} _ {g，n} $的差速器层的自旋组件的周期类别的算法。此外，我们在Sage软件包中实现它。我们的主要策略是通过将这些周期限制在$ \叠加{\ Mathcal {m}} _ {g，n} $的边界的限制中。这些限制可以通过较小的维旋转类递归计算，并通过某个线性方程系统确定原始类。为了研究偶数类型差分层边界上的旋转式，我们利用[BCCGM19]中引入的多尺度差异的模量空间。 作为我们算法的应用，可以通过使用我们的算法计算的结果来验证[CSS21]在[CSS21]中所述的自旋双重分支周期的猜想。
We construct an algorithm for computing the cycle classes of the spin components of a stratum of differentials in the moduli space of stable curves $\overline{\mathcal{M}}_{g,n}$. In addition, we implement it within the Sage package admcycles. Our main strategy is to reconstruct these cycles by their restrictions to the boundary of $\overline{\mathcal{M}}_{g,n}$ via clutching maps. These restrictions can be computed recursively by smaller dimensional spin classes and determine the original class via a certain system of linear equations. To study the spin parities on the boundary of a stratum of differentials of even type, we make use of the moduli space of multi-scale differentials introduced in [BCCGM19]. As an application of our algorithm, one can verify a conjecture on spin double ramification cycles stated in [CSS21] in many examples, by using the results computed by our algorithm.
