التفاصيل البيبلوغرافية
| العنوان: |
An Algorithm to Compute the Fundamental Classes of Spin Components of Strata of Differentials. |
| المؤلفون: |
Wong, Yiu Man |
| المصدر: |
IMRN: International Mathematics Research Notices; Mar2024, Vol. 2024 Issue 6, p4893-4962, 70p |
| مصطلحات موضوعية: |
ALGORITHMS, LINEAR equations, LINEAR systems |
| مستخلص: |
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 [ 4 ]. As an application of our algorithm, one can verify a conjecture on spin double ramification cycles stated in [ 18 ] in many examples, by using the results computed by our algorithm. [ABSTRACT FROM AUTHOR] |
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