A conjectural description of the tautological ring of the moduli space of curves

TL;DR

This paper formulates conjectures aiming to comprehensively describe the tautological ring of the moduli space of curves, providing a framework for future research and validation.

Contribution

It introduces new conjectural descriptions of the tautological ring of M_g, advancing understanding of its structure and properties.

Findings

Proposes several conjectures about the tautological ring

Discusses supporting evidence for these conjectures

Lays groundwork for future proofs and research

Abstract

The purpose of this paper is to formulate a number of conjectures giving a rather complete description of the tautological ring of M_g and to discuss the evidence for these conjectures.