Relations between tautological cycles on Jacobians
Ben Moonen

TL;DR
This paper investigates the structure of tautological cycles on Jacobians, providing new results on their ring, vanishing properties, and explicit relations, with implications for algebraic geometry and cycle theory.
Contribution
It introduces a new theorem on the tautological ring of a general curve, improving dimension calculations and cycle relations, and extends existing results to the Chow ring.
Findings
New theorem on tautological ring structure
Vanishing result for generating classes p_i
Method for explicit cycle relations
Abstract
We study tautological cycle classes on the Jacobian of a curve. We prove a new result about the ring of tautological classes on a general curve that allows, among other things, easy dimension calculations and leads to some general results about the structure of this ring. Next we obtain a vanishing result for some of the generating classes p_i; this gives an improvement of an earlier result of Herbaut. Finally we lift a result of Herbaut and van der Geer-Kouvidakis to the Chow ring (as opposed to its quotient modulo algebraic equivalence) and we give a method to obtain further explicit cycle relations. As an ingredient for this we prove a theorem about how Polishchuk's operator D lifts to the tautological subalgebra of Chow(J).
Peer Reviews
No public reviews on file for this paper yet. If you reviewed it on a platform where reviews are public (OpenReview, ICLR, NeurIPS, ICML), you can paste yours below so the community can read it here.
Videos
No videos yet. Explain this paper in a talk, walkthrough, or lecture? Add one.
Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Differential Equations and Dynamical Systems · Advanced Combinatorial Mathematics
