Towards Parallel Methods in Birational Geometry

Computational birational geometry is one of the key playing fields in an algorithmic approach to algebraic geometry, since birational maps are the fundamental way to relate algebraic varieties (or schemes). An important application is an algorithmic approach to the Minimal Model Program (MMP), which aims to classify algebraic varieties with mild singularities by finding simple birational models of such varieties in their birational equivalence class. This note presents work towards parallel methods to solve problems in birational geometry. Making use of a representation of algebraic schemes in terms of charts allows for a parallel computational approach for handling both the varieties and rational maps between them. In this note, we illustrate this approach on examples.