Projective contact log varieties

TL;DR

This paper explores contact structures on complex projective varieties with divisors, generalizing known results and detailing the structure of contractions and contact structure construction in the logarithmic setting.

Contribution

It introduces a framework for understanding contact structures on log varieties and describes elementary log contractions, extending classical results to a broader context.

Findings

Describes the structure of elementary log contractions.

Constructs contact structures on log varieties.

Generalizes non-logarithmic contact structure results.

Abstract

We study contact structures on smooth complex projective varieties with a simple normal crossing divisor, generalizing some well-known results concerning the non-logarithmic case. In particular, we describe the structure of elementary log contractions of such log varieties and we construct the corresponding contact structures.