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.
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The author is partially supported by NSF CAREER Award DMS-1350396.
