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

TL;DR

This paper classifies desingularized fiber products of semi-stable elliptic surfaces with vanishing third Betti number, which are relevant to various areas in algebraic geometry and arithmetic geometry.

Contribution

It provides a classification of these fiber products, highlighting their potential applications in the study of supersingular threefolds and Calabi-Yau degenerations.

Findings

Classification of desingularized fiber products achieved

Identification of their role in supersingular threefolds

Insights into deformation theory of trivial canonical bundle varieties

Abstract

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