A new proof of the λg conjecture in genus 2

Rogers, Taylor; Cavalieri, Renzo

doi:10.2140/involve.2024.17.465

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A new proof of the $\lambda_g$ conjecture in genus 2

Taylor Rogers and Renzo Cavalieri

Vol. 17 (2024), No. 3, 465–479

DOI: 10.2140/involve.2024.17.465

Abstract

We give a new proof of the $λ_{g}$ conjecture in genus $2$ . We use a description of the class $λ_{2}$ as a linear combination of boundary strata and show the conjecture follows inductively from applications of the projection formula, string equation, and dilaton equation.

Keywords

moduli, Hodge integrals, $\lambda_g$ conjecture, tautological classes

Mathematical Subject Classification

Primary: 14H10, 14N35

Milestones

Received: 30 November 2022

Revised: 10 March 2023

Accepted: 16 March 2023

Published: 17 July 2024

Communicated by Michael Jablonski

Authors

Taylor Rogers
Colorado State University Fort Collins, CO United States

Renzo Cavalieri
Colorado State University Fort Collins, CO United States

Vol. 17, No. 3, 2024