About the Calabi-Yau theorem and its applications
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Construction of Integral Cohomology in Some Degenerations and Its Application to Smoothing of Degenerate Calabi-yau
A smoothing theorem for normal crossings to Calabi-Yau manifolds was proved by Y. Kawamata and Y. Namikawa ([KaNa]). This paper is a study of the observation that the Picard groups and Chern classes of these Calabi-Yau manifolds are constructible from the normal crossings in such smoothings. We provide and prove the formula for the construction in its full generality and various applications ar...
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In the paper we study two types of relations: a one is between the elliptic genus of Calabi–Yau manifolds and Jacobi modular forms, another one is between the second quantized elliptic genus, Siegel modular forms and Lorentzian Kac–Moody Lie algebras. We also determine the structure of the graded ring of the weak Jacobi forms with integral Fourier coefficients. It gives us a number of applicati...
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Calabi–Yau m-folds (M,J, ω,Ω) are compact complex manifolds (M,J) of complex dimension m, equipped with a Ricci-flat Kähler metric g with Kähler form ω, and a holomorphic (m, 0)-form Ω of constant length |Ω| = 2. Using Algebraic Geometry and Yau’s solution of the Calabi Conjecture, one can construct them in huge numbers. String Theorists (a species of theoretical physicist) are very interested ...
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تاریخ انتشار 2009