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Universal Calabi-Yau Algebra: Towards an Unification of Complex Geometry

F. Anselmo·J. Ellis·D. V. Nanopoulos·G. Volkov
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Abstract

We present a universal normal algebra suitable for constructing and classifying Calabi-Yau spaces in arbitrary dimensions. This algebraic approach includes natural extensions of reflexive weight vectors to higher dimensions, related to Batyrev's reflexive polyhedra, and their n-ary combinations. It also includes a `dual' construction based on the Diophantine decomposition of invariant monomials, which provides explicit recurrence formulae for the numbers of Calabi-Yau spaces in arbitrary dimensions with Weierstrass, K3, etc., fibrations. Our approach also yields simple algebraic relations between chains of Calabi-Yau spaces in different dimensions, and concrete visualizations of their singularities related to Cartan-Lie algebras. This Universal Calabi-Yau Algebra is a powerful tool for decyphering the Calabi-Yau genome in all dimensions.

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F. Anselmo, J. Ellis, D. V. Nanopoulos, G. Volkov. 2002-07-20. Universal Calabi-Yau Algebra: Towards an Unification of Complex Geometry. https://doi.org/10.1142/s0217751x03016136

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