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arXiv · hep-th/0212272

Universal Calabi-Yau Algebra: Classification and Enumeration of Fibrations

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

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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F. Anselmo, J. Ellis, D. V. Nanopoulos, G. Volkov. 2002-12-20. Universal Calabi-Yau Algebra: Classification and Enumeration of Fibrations. https://doi.org/10.1142/s0217732303009769

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