The Construction of Numerically Calabi-Yau Orders on Projective Surfaces

TL;DR

This paper constructs many examples of maximal numerically Calabi-Yau orders on projective surfaces using a noncommutative cyclic covering technique, contributing to the understanding of their role in the Mori program.

Contribution

It introduces a noncommutative cyclic covering method to generate numerous maximal numerically Calabi-Yau orders, expanding the known examples in algebraic geometry.

Findings

Constructed a large class of maximal numerically Calabi-Yau orders

Demonstrated the effectiveness of a noncommutative cyclic covering trick

Enhanced understanding of orders in the Mori program

Abstract

In this paper, we construct a vast collection of maximal numerically Calabi-Yau orders utilising a noncommutative analogue of the well-known commutative cyclic covering trick. Such orders play an integral role in the Mori program for orders on projective surfaces and although we know a substantial amount about them, there are relatively few known examples.