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

Georgios Politopoulos; Adrien Sauvaget

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arXiv · 2206.00358

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

Georgios Politopoulos·Adrien Sauvaget

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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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Georgios Politopoulos, Adrien Sauvaget. 2022-06-01. Computation of $\lambda$-classes via strata of differentials. https://arxiv.org/abs/2206.00358

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