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

Hokuto Uehara

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

Algebraic Geometry 2009-11-13 v2

Authors: Hokuto Uehara

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.

Keywords

Fourier-Mukai transforms birational Torelli problem rational elliptic surfaces derived equivalence deformation equivalence minimal 3-folds

Cite

@article{arxiv.0904.0303,
  title  = {A counterexample of the birational Torelli problem via Fourier--Mukai transforms},
  author = {Hokuto Uehara},
  journal= {arXiv preprint arXiv:0904.0303},
  year   = {2009}
}

Comments

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

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

Abstract

Keywords

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