Desingularized fiber products of semi-stable elliptic surfaces with vanishing third Betti number

摘要

Desingularized fiber products of semi-stable, non-isotrivial jacobianelliptic surfaces with vanishing third Betti number are classified. Suchvarieties may play a role in the study of supersingular threefolds, of thedeformation theory of varieties with trivial canonical bundle, and of thearithmetic degenerations of rigid Calabi-Yau threefolds.