On the construction of Calabi-Yau operators

TL;DR

This paper explores methods to construct Calabi-Yau differential operators by applying geometric-preserving operations, leading to new and known examples relevant in mathematical physics and algebraic geometry.

Contribution

It introduces a systematic approach to generate Calabi-Yau operators through sequences of geometric operations, expanding the toolkit for researchers in the field.

Findings

Constructed new Calabi-Yau operators using sequences of geometric operations.

Identified classes of operators that preserve Calabi-Yau properties.

Provided examples demonstrating the effectiveness of the method.

Abstract

Given a differential operator of geometric origin there exists a list of operations that preserve this property, e.g., tensor products, pull-backs, push-forwards and the middle convolution. We apply certain sequences of these operations to construct known and new examples of Calabi-Yau operators.