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arXiv · 1206.3783

On the tautological rings of M_{g, 1} and its universal Jacobian

Qizheng Yin
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Abstract

We give a new method of producing relations in the tautological ring R(M_{g, 1}), using the sl_2-action on the Chow ring of the universal Jacobian. With these relations, we prove that R(M_{g, 1}) is generated by κ_i for i no greater than g/3, together with ψ. Our computation shows that Faber's conjectures for M_{g, 1} are true for g up to 19. Further, by pushing relations forward to M_g, we obtain a new proof of Faber's conjectures (for M_g) for g up to 23. For g = 24, our method recovers all the Faber-Zagier relations. We also give an algebraic proof of an identity of Morita.

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Qizheng Yin. 2012-07-30. On the tautological rings of M_{g, 1} and its universal Jacobian. https://arxiv.org/abs/1206.3783

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