Relations in the tautological ring of the universal curve

We bound the dimensions of the graded pieces of the tautological ring of the universal curve from below for genus up to $27$ and from above for genus up to $9$. As a consequence we obtain the precise structure of the tautological ring of the universal curve for genus up to $9$. In particular, we see that it is Gorenstein for these genera.

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Received 22 April 2017

Accepted 3 September 2019

Published 14 December 2022