Specially defined Calabi-Yau manifolds having the hypersurfaces of degree - 5 in ℙ⁴ satisfying the non-trivial canonical bundle Λˣ₃ where the embedding holomorphic map ψ∶ X⟶ ℙ with the Kähler form for holomorphic line bundle giving a strictly positive parameter ℓᵏ ⨂ ∃k > 0 representing ℓ through the first Chern Class H² (2,ℤ). When for every Kähler Class , the Cohomology class exists with the compact form (X,ω) ∀ potential spaces satisfying H²ₔᵣ (X) with the ∂∂*−lemma for a harmonic form giving us the (1,1)⁺ − Kähler potential 𝒊2⁻¹∂∂*ρ. Taking all this in effect and making it established through various conjectures, axioms, ideals, theorems – an equivalence class is shown between the structures: Kahler-Manifold, Calabi-Yau-Manifold, Hyperkahler-Manifold, Quintic-3-Fold, Kummer Surface, K–3 Surface, De Rahm Cohomology Class (Hol(Ω(μ,ν)). The extreme case considered here is the exclusion of Complex hyperbolic Kahler – represented by ℂℙⁿ ∀n = -1. In course of making this paper the non–trivial aspects concerning the topological structures in aspects of string theory, the compact Kahler with a Ricci–flatness explained here.
Parameterizing the diagonal points for each orbit +∓ and other —= over 𝒅𝒆𝒈₂ topologies considering the minimum genus 1 with marked points 2² over stabilizer moduli η when composed under loads or vibrations positive-∂ - negative-∂̅ - null-neutral-∂̅∂̅̅̅ from neutral-∂∂̅ phase alters the state ω to ω⋆ induces a change in genus geometries from rings at the mouth being hyperbolic σ× inside to hyperbolic or elliptic or Euclidean σ outside transits the function acting on the topology ⋆∶ω⟶ω⋆ suspends the surface by deforming stabilizer moduli η except in case of null-neutral-∂̅∂̅̅̅ ̅ iff class [ζ] is satisfied. Higher 𝒅𝒆𝒈 generalizations are not taken for this paper.
<p>Equivalence, duality, and invariance are the pin-points of unification in modern theoretical physics that got the twist of topologies when going beyond the notions of differential and conformal domains to geometries to the symplectic norm of topologies with the pillars being the algebraic geometry taking the counting of specified states through the Enumerative ones.</p>
A segregated approach is used through several maps and classifiers where a study has been conducted to establish a concrete relational equivalence among several hypercomplex structures over three—order categorization tables namely ‘Enrique surface classification’ and ‘Enrique-K3-Complex(K3)-Kähler-Kummer surface characteristics’ with ‘K3– Complex(K3)-Kähler-Kummer(K3)-Kummer classifiers’ taking into account several notions of algebraic topology and algebraic geometry. This paper is the continuation of the previous preprint https://doi.org/10.21203/rs.3.rs-1635957/v1. For the Enrique 7—classifiers are considered namely I, II, III, IV, V, VI, VII.
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