2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/78734In 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 applications to the theory of elliptic genus and of the second quantized elliptic genus.To appear in Algebra i Analiz (St. Petersburg Math. Journal) 11:5 (1999); AMS-TeX, 25 pagesAlgebraic GeometryHigh Energy Physics - TheoryAlgebraic Topologytext