2012/06/17 by Qizheng Yin, Yin, Qizheng · 3 citations
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #Nonlinear Waves and Solitons #math.AG #msc:14C25 #msc:14H10 #msc:14H40
paper · pdf · doi:10.48550/arxiv.1206.3783
22 pages, 3 figures. v2: fixed errors in Table 1; added an appendix by Li Ma explaining computational details
arxiv created 2012/07/30 · arxiv updated 2012/07/31
We give a new method of producing relations in the tautological ring R(Mg, 1), using the sl2-action on the Chow ring of the universal Jacobian. With these relations, we prove that R(Mg, 1) is generated by κi for i no greater than g/3, together with ψ. Our computation shows that Faber's conjectures for Mg, 1 are true for g up to 19. Further, by pushing relations forward to Mg, we obtain a new proof of Faber's conjectures (for Mg) 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.