An algorithm to compute fundamental classes of spin components of strata of differentials

Yiu Man Wong

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arXiv · 2211.16061

An algorithm to compute fundamental classes of spin components of strata of differentials

Yiu Man Wong

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Abstract

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.

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Yiu Man Wong. 2022-11-29. An algorithm to compute fundamental classes of spin components of strata of differentials. https://arxiv.org/abs/2211.16061

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