Universal Calabi-Yau Algebra: Classification and Enumeration of Fibrations

Details Universal Calabi-Yau Algebra: Classification and Enumeration of Fibrations Universal Calabi-Yau Algebra: Classification and Enumeration of Fibrations

2002-12-20

arxiv.org/abs/hep-th/0212272v1

Mod.Phys.Lett.A18:699-710,2003

Physics

High Energy Physics

High Energy Physics - Theory

17 pages, 2 figures

Scientific paper

10.1142/S0217732303009769

We apply a universal normal Calabi-Yau algebra to the construction and classification of compact complex $n$-dimensional spaces with SU(n) holonomy and their fibrations. This algebraic approach includes natural extensions of reflexive weight vectors to higher dimensions and a `dual' construction based on the Diophantine decomposition of invariant monomials. The latter provides recurrence formulae for the numbers of fibrations of Calabi-Yau spaces in arbitrary dimensions, which we exhibit explicitly for some Weierstrass and K3 examples.

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