Logarithmic Embeddings and Logarithmic Semistable Reductions

TL;DR

This paper establishes a criterion for logarithmic embeddings in normal crossing varieties and provides a new proof for the Kawamata--Namikawa theorem on log structures of semistable type, advancing understanding in algebraic geometry.

Contribution

It introduces a new criterion for logarithmic embeddings and offers a novel proof of the Kawamata--Namikawa theorem, enhancing theoretical tools in log geometry.

Findings

Established a criterion for logarithmic embeddings in normal crossing varieties.

Provided a new proof of the Kawamata--Namikawa theorem on log structures.

Contributed to the theoretical foundation of logarithmic geometry.

Abstract

In this paper, we give a criterion for the existence of logarithmic embeddings -- which was first introduced by Steenbrink -- for general normal crossing varieties. Using this criterion, we also give a new proof of the theorem of Kawamata--Namikawa which states a criterion for the existence of the log structures of semistable type.