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• W3121556270 abstract "We bound from below the complexity of the top Chern class $lambda _g$ of the Hodge bundle in the Chow ring of the moduli space of curves: no formulas for $lambda _g$ in terms of classes of degrees 1 and 2 can exist. As a consequence of the Torelli map, the 0-section over the second Voronoi compactification of the moduli of principally polarized abelian varieties also cannot be expressed in terms of classes of degree 1 and 2. Along the way, we establish new cases of Pixton's conjecture for tautological relations. In the log Chow ring of the moduli space of curves, however, we prove $lambda _g$ lies in the subalgebra generated by logarithmic boundary divisors. The proof is effective and uses Pixton's double ramification cycle formula together with a foundational study of the tautological ring defined by a normal crossings divisor. The results open the door to the search for simpler formulas for $lambda _g$ on the moduli of curves after log blow-ups." @default.
• W3121556270 created "2021-02-01" @default.
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• W3121556270 date "2023-02-01" @default.
• W3121556270 modified "2023-09-25" @default.
• W3121556270 title "The Hodge bundle, the universal 0-section, and the log Chow ring of the moduli space of curves" @default.
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• W3121556270 doi "https://doi.org/10.1112/s0010437x22007874" @default.
• W3121556270 hasPublicationYear "2023" @default.
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