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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...

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Autores principales: Anselmo, F., Ellis, John R., Nanopoulos, Dimitri V., Volkov, G.
Lenguaje:eng
Publicado: 2002
Materias:
Acceso en línea:https://dx.doi.org/10.1142/S0217751X03016136
http://cds.cern.ch/record/572303
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author Anselmo, F.
Ellis, John R.
Nanopoulos, Dimitri V.
Volkov, G.
author_facet Anselmo, F.
Ellis, John R.
Nanopoulos, Dimitri V.
Volkov, G.
author_sort Anselmo, F.
collection CERN
description 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.
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spelling cern-5723032023-03-14T17:04:57Zdoi:10.1142/S0217751X03016136http://cds.cern.ch/record/572303engAnselmo, F.Ellis, John R.Nanopoulos, Dimitri V.Volkov, G.Universal Calabi-Yau Algebra: Towards an Unification of Complex GeometryParticle Physics - TheoryWe 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.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/0207188CERN-TH-2001-380ACT-06-02CPT-TAMU-16-02CERN-TH-2001-380ACT-2002-006CPT-TAMU-2002-16oai:cds.cern.ch:5723032002-07-20
spellingShingle Particle Physics - Theory
Anselmo, F.
Ellis, John R.
Nanopoulos, Dimitri V.
Volkov, G.
Universal Calabi-Yau Algebra: Towards an Unification of Complex Geometry
title Universal Calabi-Yau Algebra: Towards an Unification of Complex Geometry
title_full Universal Calabi-Yau Algebra: Towards an Unification of Complex Geometry
title_fullStr Universal Calabi-Yau Algebra: Towards an Unification of Complex Geometry
title_full_unstemmed Universal Calabi-Yau Algebra: Towards an Unification of Complex Geometry
title_short Universal Calabi-Yau Algebra: Towards an Unification of Complex Geometry
title_sort universal calabi-yau algebra: towards an unification of complex geometry
topic Particle Physics - Theory
url https://dx.doi.org/10.1142/S0217751X03016136
http://cds.cern.ch/record/572303
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