Adjoint Computation for Hypersurfaces Using Formal Desingularizations

TL;DR

This paper introduces a method using formal desingularizations to compute adjoint sections of twisted pluricanonical sheaves, aiding in the birational classification of algebraic schemes.

Contribution

It presents a novel approach leveraging formal desingularizations for calculating adjoint sections, enhancing tools for scheme classification.

Findings

Effective computation of adjoint sections via formal desingularizations

Applications to birational classification of schemes

Extension of previous theoretical frameworks

Abstract

We show how to use formal desingularizations (defined earlier by the first author) in order to compute the global sections (also called adjoints) of twisted pluricanonical sheaves. These sections define maps that play an important role in the birational classification of schemes.