Non-birational Calabi-Yau threefolds that are derived equivalent

2006/01/10 by Caldararu, Andrei
#14E30 #14F05 #14J32 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.math/0601232

Abstract

We argue that the existence of genus one fibrations with multisections of high degree on certain Calabi-Yau threefolds implies the existence of pairs of such varieties that are not birational, but are derived equivalent. It also (likely) implies the existence of non-birational counterexamples to the Torelli problem for Calabi-Yau threefolds.

Related

• New counterexamples to the birational Torelli theorem for Calabi--Yau manifolds
• Connecting certain rigid birational non-homeomorphic Calabi--Yau threefolds via Hilbert scheme
• Flops and derived categories
• A Finiteness Theorem for Elliptic Calabi-Yau Threefolds
• On Calabi-Yau threefolds with large nonabelian fundamental groups