Physics – High Energy Physics – High Energy Physics - Theory
Scientific paper
2000-02-12
Phys.Part.Nucl.32:318-375,2001; Fiz.Elem.Chast.Atom.Yadra 32:605-698,2001
Physics
High Energy Physics
High Energy Physics - Theory
87 pages LaTeX, 16 eps figures, uses header.tex (included)
Scientific paper
We present an inductive algebraic approach to the systematic construction and classification of generalized Calabi-Yau (CY) manifolds in different numbers of complex dimensions, based on Batyrev's formulation of CY manifolds as toric varieties in weighted complex projective spaces associated with reflexive polyhedra. We show how the allowed weight vectors in lower dimensions may be extended to higher dimensions, emphasizing the roles of projection and intersection in their dual description, and the natural appearance of Cartan-Lie algebra structures. The 50 allowed extended four-dimensional vectors may be combined in pairs (triples) to form 22 (4) chains containing 90 (91) K3 spaces, of which 94 are distinct, and one further K3 space is found using duality. In the case of CY_3 spaces, pairs (triples) of the 10~270 allowed extended vectors yield 4242 (259) chains with K3 (elliptic) fibers containing 730 additional K3 polyhedra. A more complete study of CY_3 spaces is left for later work.
Anselmo Franco
Ellis John
Nanopoulos Dimitri V.
Volkov Gennady
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