Classification of weighted graphs up to blowing-up and blowing-down

TL;DR

This paper classifies weighted forests based on blowing-up and blowing-down operations, which are important for understanding the structure of algebraic surfaces.

Contribution

It provides a classification framework for weighted forests considering these operations, advancing the study of algebraic surfaces.

Findings

Classification of weighted forests achieved

Identification of invariants under blowing-up/down

Applications to algebraic surface theory

Abstract

We classify weighted forests up to the blowing-up and blowing-down operations which are relevant for the study of algebraic surfaces.