A counterexample of the birational Torelli problem via Fourier--Mukai transforms
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, h1( O)=h2( 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.
0
Turn this paper into a lesson
ArcXiv compiles a structured reading guide from this paper's metadata: plain-English importance, contributions, prerequisite concepts, which sections to read first, flashcards, and a quiz. Grounded in the abstract, never invented.