Compositio Mathematica

Research Article

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

Chad Schoena1

a1 Department of Mathematics, Duke University, Box 90320, Durham, NC 27708-0320, USA (email: schoen@math.duke.edu)

Abstract

Desingularized fiber products of semi-stable elliptic surfaces with Hetale3=0 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 arithmetic degenerations of rigid Calabi–Yau threefolds.

(Received November 21 2007)

(Accepted June 04 2008)

2000 Mathematics Subject Classification

  • 14D06;
  • 14J32;
  • 14G15

Keywords

  • supersingular threefold;
  • Calabi–Yau threefold;
  • fiber product of elliptic surfaces

Footnotes

Partial support by the NSF (DMS-0200012) and NSA (MDA904-97-1-0041) is gratefully acknowledged.