arXiv subjects

F. Anselmo

Publications and source records attributed to F. Anselmo.

4 recordsLinked to original sources

arXiv2002

Universal Calabi-Yau Algebra: Classification and Enumeration of Fibrations

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.

hep-th↗

arXiv2002

Universal Calabi-Yau Algebra: Towards an Unification of Complex Geometry

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.

hep-th↗

arXiv2000

Results from an Algebraic Classification of Calabi-Yau Manifolds

We present results from an inductive algebraic approach to the systematic construction and classification of the `lowest-level' CY3 spaces defined as zeroes of polynomial loci associated with reflexive polyhedra, derived from suitable vectors in complex projective spaces. These CY3 spaces may be sorted into `chains' obtained by combining lower-dimensional projective vectors classified previously. We analyze all the 4242 (259, 6, 1) two- (three-, four-, five-) vector chains, which have, respectively, K3 (elliptic, line-segment, trivial) sections, yielding 174767 (an additional 6189, 1582, 199) distinct projective vectors that define reflexive polyhedra and thereby CY3 spaces, for a total of 182737. These CY3 spaces span 10827 (a total of 10882) distinct pairs of Hodge numbers h_11, h_12. Among these, we list explicitly a total of 212 projective vectors defining three-generation CY3 spaces with K3 sections, whose characteristics we provide.

hep-th↗

arXiv2000

Towards an Algebraic Classification of Calabi-Yau Manifolds I: Study of K3 Spaces

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.

hep-th↗