A counterexample of the birational Torelli problem via Fourier--Mukai transforms
arXiv:0904.0303
Abstract
We study the Fourier--Mukai numbers of rational elliptic surfaces. As its application, we give an example of a pair of minimal 3-folds with Kodaira dimensions 1, $h^1(\mc O)=h^2(\mc O)=0$ such that they are mutually derived equivalent, deformation equivalent, but not birationally equivalent. It also supplies a counterexample of the birational Torelli problem.
21 pages. Theorem 1.1 becomes weaker, since the proof of Lemma 2.5 in v1 is incorrect. Title has been changed. To appear in Journal of Algebraic Geometry