2024/06/15 by Samir Canning, Canning, Samir
Mathematics · #14C15 #14C17 #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2406.10516
openalex publication_date 2024/06/15 · openalex created_date 2024/06/19 · openalex updated_date 2026/07/28
We prove that the tautological rings R^*(Mg,n) and RH^*(Mg,n) are not Gorenstein when g≥ 2 and 2g+n≥ 24, extending results of Petersen and Tommasi in genus 2. The proof uses the intersection of tautological classes with non-tautological bielliptic cycles. We conjecture the converse: the tautological rings should be Gorenstein when g=0,1 or g≥ 2 and 2g+n<24. The conjecture is known for g=0,1 by work of Keel and Petersen, and we prove several new cases of this conjecture for RH^*(Mg,n) when g≥ 2.