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

Uehara, Hokuto

doi:10.1090/S1056-3911-2011-00551-1

Author: Hokuto Uehara
Journal: J. Algebraic Geom. 21 (2012), 77-96
DOI: https://doi.org/10.1090/S1056-3911-2011-00551-1
Published electronically: March 23, 2011
MathSciNet review: 2846680
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Abstract | References | Additional Information

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 $1$, $h^1(\mathcal O)=h^2(\mathcal O)=0$ 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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Additional Information

Hokuto Uehara
Affiliation: Department of Mathematics and Information Sciences, Tokyo Metropolitan University, 1-1 Minamiohsawa, Hachioji-shi, Tokyo, 192-0397, Japan
MR Author ID: 663390
Email: hokuto@tmu.ac.jp

Received by editor(s): April 2, 2009
Received by editor(s) in revised form: October 5, 2009
Published electronically: March 23, 2011
Additional Notes: I am supported by the Grants-in-Aid for Scientific Research (No. 20740022).