# Log surfaces of Picard rank one from four lines in the plane

## TL;DR

This paper provides formulas for numerical invariants of certain singular surfaces derived from four-line configurations in the plane, and identifies extremal volume properties among these surfaces.

## Contribution

It introduces explicit formulas for invariants of log surfaces with Picard rank one from four-line arrangements and determines their minimal volume and accumulation points.

## Key findings

- Derived formulas for invariants of these surfaces
- Identified the smallest positive volume among these surfaces
- Established the smallest accumulation point of their volumes

## Abstract

We derive simple formulas for the basic numerical invariants of a singular surface with Picard number one obtained by blowups and contractions of the four-line configuration in the plane. As an application, we establish the smallest positive volume and the smallest accumulation point of volumes of log canonical surfaces obtained in this way.