Mirror Symmetry and Projective Geometry of Fourier-Mukai Partners
Shinobu Hosono, Hiromichi Takagi
TL;DR
This survey explores the relationship between mirror symmetry and Fourier-Mukai partners in Calabi-Yau threefolds and K3 surfaces, highlighting recent research developments in algebraic geometry.
Contribution
It consolidates recent findings on mirror symmetry and Fourier-Mukai partners for Calabi-Yau threefolds with Picard number one and K3 surfaces.
Findings
Summary of mirror symmetry phenomena in Calabi-Yau threefolds
Characterization of Fourier-Mukai partners in specific geometric contexts
Connections between mirror symmetry and derived categories
Abstract
This is a survey article on mirror symmetry and Fourier-Mukai partners of Calabi-Yau threefolds with Picard number one based on recent works by the authors [HoTa1,2,3,4]. For completeness, mirror symmetry and Fourier-Mukai partners of K3 surfaces are also discussed.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Algebra and Geometry · Geometry and complex manifolds