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Tautological ring of strata of differentials. (English) Zbl 1408.14094
Dans cette note, l’auteur étudie l’anneau tautologique des strates de pluridifférentielles. Cet anneau est généré par le tiré en arrière des classes \(\kappa\) de Miller-Morita-Mumford, des fibrés cotangents aux points marqués \(\psi\) et par \(\eta= \mathcal{O}(-1)\). Le résultat principal est le suivant: Si la strate considérée paramètre des \(k\)-différentielles sans pôles d’ordre \(-k\), alors l’anneau tautologique de cette strate est généré par \(\eta\). Si les \(k\)-différentielles possèdent des pôles d’ordre \(-k\), alors l’anneau tautologique est généré par le tiré en arrière des classes \(\psi\) correspondant à ces points. De nombreux exemples sont donnés pour montrer que ce résultat est optimal.
MSC:
14H10 Families, moduli of curves (algebraic)
14H15 Families, moduli of curves (analytic)
14C25 Algebraic cycles
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