Neron-Severi group for nonalgebraic elliptic surfaces I. Elliptic bundle case.
Let be a field and be the Grassmannian of -dimensional linear subspaces of . A map is called nesting if for every . Glover, Homer and Stong showed that there are no continuous nesting maps except for a few obvious ones. We prove a similar result for algebraic nesting maps , where is an algebraically closed field of arbitrary characteristic. For this yields a description of the algebraic sub-bundles of the tangent bundle to the projective space .
The aim of this article is to present five new examples of modular rigid Calabi-Yau threefolds by giving explicit correspondences to newforms of weight 4 and levels 10, 17, 21 and 73.