Polynomial deformations and cohomology of Calabi-Yau manifolds (Q1096198)

The authors show that the polynomial deformation method (PDM) that is used in the physics literature to determine the Hodge numbers of compact Ricci-flat Kähler manifolds (Calabi-Yau manifolds) does not really depend on the Kodaira-Spencer deformation theory but on a simple cohomology computation which is, however, not universally valid. They present a general analysis which applies to all Calabi-Yau manifolds embedded as complete intersections in products of complex projective spaces, yields sufficient conditions for the validity of PDM, and provides an alternative computation of all the Hodge numbers in many cases in which PDM fails.