A counterexample of the birational Torelli problem via Fourier--Mukai transforms

Details A counterexample of the birational Torelli problem via Fourier--Mukai transforms A counterexample of the birational Torelli problem via Fourier--Mukai transforms

2009-04-02

arxiv.org/abs/0904.0303v2

Mathematics

Algebraic Geometry

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 Jo

Scientific paper

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.

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