1997/11/03 by Carel Faber, Faber, Carel F.
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.math/9711219
openalex publication_date 1997/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Looijenga recently proved that the tautological ring of Mg vanishes in degree d>g-2 and is at most one-dimensional in degree g-2, generated by the class of the hyperelliptic locus. Here we show that Kg-2 is non-zero on Mg. The proof uses the Witten conjecture, proven by Kontsevich. With similar methods, we expect to be able to prove some (possibly all) of the identities in degree g-2 in the tautological ring that are part of the author's conjectural explicit description of the ring.