Computation of $\lambda$-classes via strata of differentials - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2022

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

Résumé

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.

Dates et versions

hal-03835407 , version 1 (31-10-2022)

Identifiants

Citer

Georgios Politopoulos, Adrien Sauvaget. Computation of $\lambda$-classes via strata of differentials. 2022. ⟨hal-03835407⟩
9 Consultations
0 Téléchargements

Altmetric

Partager

More