On K3 fibrations: towards mirror symmetry
Cristina Mart\'inez Ram\'irez
TL;DR
This paper explores K3 fibrations over one-dimensional bases, characterizing their mirror duals through derived equivalences, thereby advancing the understanding of mirror symmetry in the context of Calabi-Yau fibrations.
Contribution
It provides a characterization of the mirror duals of K3 fibrations as derived equivalent Calabi-Yau fibrations, linking moduli spaces and mirror symmetry.
Findings
Mirror duals are derived equivalent Calabi-Yau fibrations.
The dual fibration corresponds to a component of the moduli space of sheaves.
The work connects K3 fibrations with mirror symmetry via derived categories.
Abstract
Given X a K3 surface, a mirror dual to X can be identified with a component of the moduli space of semistable sheaves on X. We consider fibrations by K3 surfaces over a one dimensional base that are Calabi-Yau and we charaterize the dual fibration that turns to be derived equivalent to the original one relating the problem to mirror symmetry.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Geometric and Algebraic Topology · Advanced Algebra and Geometry