Relations in the Tautological Ring of the Universal Curve

2020/07/31 by Olof Bergvall, Bergvall, Olof
Mathematics · #14H10 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2007.15972

openalex publication_date 2020/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Citations

• Relations in the tautological ring of the moduli space of curves
• Conjectural relations in the tautological ring of M_g,n
• Relations in the tautological ring
• On the tautological rings of M_{g, 1} and its universal Jacobian
• Tautological relations in moduli spaces of weighted pointed curves

Related

• On the tautological ring of M_g,n
• Relations in the tautological ring
• A conjectural description of the tautological ring of the moduli space of curves
• Cycles on curves and Jacobians: a tale of two tautological rings
• Universal algebraic equivalences between tautological cycles on Jacobians of curves