Derived equivalences of Calabi-Yau fibrations
Cristina Martinez Ramirez, Andrey Todorov
TL;DR
This paper explores Calabi-Yau fibrations by abelian and K3 surfaces, establishing derived equivalences between dual fibrations and connecting the findings to mirror symmetry concepts.
Contribution
It introduces a method to construct dual Calabi-Yau fibrations that are derived equivalent, linking geometric duality with mirror symmetry.
Findings
Dual fibrations are derived equivalent to original fibrations.
The approach relates geometric duality to mirror symmetry.
Provides new insights into Calabi-Yau fibration structures.
Abstract
We consider fibrations by abelian surfaces and K3 surfaces over a one dimensional base that are Calabi-Yau and we obtain dual fibrations that are derived equivalent to the original fibration. Finally, we relate the problem to mirror symmetry.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric and Algebraic Topology · Geometry and complex manifolds