Logarithmic cohomological field theories

TL;DR

This paper introduces a new logarithmic structure on the moduli stack of stable curves, enabling the definition of refined cohomological field theories in logarithmic Chow cohomology, and realizes the double ramification cycle within this framework.

Contribution

It develops a novel logarithmic structure on moduli stacks and constructs refined cohomological field theories valued in logarithmic Chow cohomology.

Findings

Defined logarithmic gluing maps on moduli stacks.

Constructed logarithmic cohomological field theories.

Realized the double ramification cycle as a partial logarithmic cohomological field theory.

Abstract

We introduce a new logarithmic structure on the moduli stack of stable curves, admitting logarithmic gluing maps. Using this we define cohomological field theories taking values in the logarithmic Chow cohomology ring, a refinement of the usual notion of a cohomological field theory. We realise the double ramification cycle as a partial logarithmic cohomological field theory.