Universal CalabiYau Algebra:
Abstract
We present a universal normal algebra suitable for constructing and classifying CalabiYau 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 nary combinations. It also includes a "dual" construction based on the Diophantine decomposition of invariant monomials, which provides explicit recurrence formulae for the numbers of CalabiYau spaces in arbitrary dimensions with Weierstrass, K3, etc., fibrations. Our approach also yields simple algebraic relations between chains of CalabiYau spaces in different dimensions, and concrete visualizations of their singularities related to CartanLie algebras. This Universal CalabiYau algebra is a powerful tool for deciphering the CalabiYau genome in all dimensions.
 Publication:

International Journal of Modern Physics A
 Pub Date:
 2003
 DOI:
 10.1142/S0217751X03016136
 arXiv:
 arXiv:hepth/0207188
 Bibcode:
 2003IJMPA..18.5541A
 Keywords:

 Infinite series of CalabiYau spaces;
 universal algebra;
 holomorphic fibre bundle structure;
 High Energy Physics  Theory
 EPrint:
 81 pages LaTeX, 8 eps figures