Tautological ring of strata of differentials

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Abstract

Strata of k-differentials on smooth curves parameterize sections of the k-th power of the canonical bundle with prescribed orders of zeros and poles. Define the tautological ring of the projectivized strata using the \(\kappa \) and \(\psi \) classes of moduli spaces of pointed smooth curves along with the class \(\eta = \mathcal O(-1)\) of the Hodge bundle. We show that if there is no pole of order k, then the tautological ring is generated by \(\eta \) only, and otherwise it is generated by the \(\psi \) classes corresponding to the poles of order k.

Mathematics Subject Classification

14H10 14H15 14C25 

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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsBoston CollegeChestnut HillUSA

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