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Computation of $\lambda$-classes via strata of differentials

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arxiv 2206.00358 v1 pith:64COECNO submitted 2022-06-01 math.AG

Georgios Politopoulos , Adrien Sauvaget This is my paper · ORCID
classification math.AG
keywords classclassesrelationsbundlechernexpressedhodgestable
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abstract

We introduce a new family of tautological relations of the moduli space of stable curves of genus $g$. These relations are obtained by computing the Poincar\'e-dual class of empty loci in the Hodge bundle. We use these relations to obtain a new expression for the Chern classes of the Hodge bundle. We prove that the $(g-i)$th class can be expressed as a linear combination of tautological classes involving only stable graphs with at most $i$ loops. In particular the top Chern class may be expressed with trees. This property was expected as a consequence of the DR/DZ equivalence conjecture by Buryak-Gu\'er\'e-Rossi.

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  1. DR cycles and strata of differentials with spin parity

    math.AG 2025-09 conditional novelty 8.0 of 10

    The parity-refined classes of strata of k-differentials are tautological and explicitly computable, via a spin double ramification cycle formula and Segre classes of cones of spin sections.

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