Mirror constructions for K3 surfaces from bimodal singularities
Makiko Mase, Ursula Whitcher
TL;DR
This paper investigates lattice polarizations of K3 surfaces derived from bimodal singularities, revealing limitations of mirror lattices and identifying mirror sublattices through toric variety embeddings.
Contribution
It introduces a novel analysis of lattice polarizations for K3 surfaces from bimodal singularities and clarifies the mirror lattice structure within toric compactifications.
Findings
Polarizations from toric embeddings are not mirror lattices.
Mirror sublattices can be explicitly identified.
The study advances understanding of mirror symmetry in K3 surfaces.
Abstract
We study lattice polarizations of five exceptional pairs of families of K3 surfaces obtained via compactifications of strange dual pairs of bimodal singularities. We show that the polarizations induced by embedding these paired families in paired toric varieties obtained from polar dual reflexive polytopes cannot be mirror lattices and identify mirror sublattices.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Advanced Combinatorial Mathematics · Advanced Algebra and Geometry