About a class of Calabi-Yau differential equations
Gert Almkvist, Michael Bogner, Jes\'us Guillera
TL;DR
This paper introduces an experimental approach to identify Calabi-Yau differential equations of orders 3, 5, and 7, linking them to modular functions and geometric invariants, expanding understanding of their structure.
Contribution
It presents a new experimental method for finding Calabi-Yau differential equations of orders 3 and 5, and explores examples of order 7, proposing conjectures on geometric invariants.
Findings
Identified Calabi-Yau differential equations of order 3 related to modular functions.
Constructed examples of order 5 Calabi-Yau differential equations.
Provided initial examples of order 7 Calabi-Yau differential equations.
Abstract
We explain an experimental method to find CY-type differential equations of order related to modular functions of genus zero. We introduce a similar class of Calabi-Yau differential equations of order , show several examples and make a conjecture related to some geometric invariants. We finish the paper with a few examples of seven order.
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Taxonomy
TopicsNonlinear Waves and Solitons · Advanced Mathematical Identities · Algebraic Geometry and Number Theory