Stable logarithmic maps to Deligne--Faltings pairs II

TL;DR

This paper extends the theory of stable logarithmic maps to a broader class of Deligne--Faltings pairs, showing how complex cases can be derived from simpler foundational cases.

Contribution

It introduces a method to construct algebraic stacks of log maps for generalized Deligne--Faltings structures from basic cases with Cartier divisors.

Findings

Existence of algebraic stacks of log maps for generalized Deligne--Faltings pairs.

Reduction of complex cases to simple normal crossings divisor cases.

Framework applicable to a wide class of log structures.

Abstract

We make an observation which enables one to deduce the existence of an algebraic stack of log maps for all generalized Deligne--Faltings log structures (in particular simple normal crossings divisor) from the simplest case with log structures given by a Cartier divisor (essentially the smooth divisor case).