On the construction of Calabi-Yau operators

2025/08/05 by Reiter, Stefan
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.03299

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.

Citations

• On the Hodge theory of the additive middle convolution
• Classifying (almost)-Belyi maps with Five Exceptional Points
• Some fourth order CY-type operators with non symplectically rigid\n monodromy
• On symplectically rigid local systems of rank four and Calabi-Yau\n operators
• A rigid irregular connection on the projective line
• Genus Zero Modular Functions
• Tables of Calabi--Yau equations

Related

• The art of finding Calabi-Yau differential eq1uations
• Calabi-Yau operators of degree two
• Notes on Calabi-Yau ordinary differential equations
• Calabi--Yau Operators
• Differential algebra on lattice Green functions and Calabi-Yau operators (unabridged version)