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arXiv · 1708.00519

Tautological ring of strata of differentials

Dawei Chen
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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 tautological class $\eta$ 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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Dawei Chen. 2017-08-01. Tautological ring of strata of differentials. https://arxiv.org/abs/1708.00519

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