Universal Calabi-Yau Algebra: Towards an Unification of Complex Geometry
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.
Keywords
Cite
@article{arxiv.hep-th/0207188,
title = {Universal Calabi-Yau Algebra: Towards an Unification of Complex Geometry},
author = {F. Anselmo and J. Ellis and D. V. Nanopoulos and G. Volkov},
journal= {arXiv preprint arXiv:hep-th/0207188},
year = {2009}
}
Comments
81 pages LaTeX, 8 eps figures