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 deciphering the Calabi-Yau genome in all dimensions.
International Journal of Modern Physics A
- Pub Date:
- Infinite series of Calabi-Yau spaces;
- universal algebra;
- holomorphic fibre bundle structure;
- High Energy Physics - Theory
- 81 pages LaTeX, 8 eps figures