2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/68301We construct a spectral sequence that converges to the cohomology of the chiral de Rham complex over a Calabi-Yau hypersurface and whose first term is a vertex algebra closely related to the Landau-Ginburg orbifold. As an application, we prove an explicit orbifold formula for the elliptic genus of Calabi-Yau hypersurfaces.Latex, 50p. Some typos corrected, the page size may have been fixed. One new result, a theorem on the vertx algebra structure of the Landau-Ginzburg orbifold appears in sect. 5.2.18. This is the final version to appear in the Moscow Mathematical JournalAlgebraic GeometryMathematical PhysicsGeometric TopologyAlgebraic Geometry; Algebraic Topology; Mathematical Physicstext