A note on homological mirror symmetry for singularities of type D
Masahiro Futaki, Kazushi Ueda
TL;DR
This paper establishes homological mirror symmetry for certain Lefschetz fibrations constructed from polynomials of types A and D, advancing understanding of mirror symmetry in singularity theory.
Contribution
It proves homological mirror symmetry for Lefschetz fibrations formed from sums of type A and D polynomials, analyzing Fukaya categories under type D polynomial addition.
Findings
Homological mirror symmetry holds for these specific Lefschetz fibrations.
Behavior of Fukaya categories under type D polynomial addition is characterized.
Results extend mirror symmetry understanding to new classes of singularities.
Abstract
We prove homological mirror symmetry for Lefschetz fibrations obtained as disconnected sums of polynomials of types A or D. The proof is based on the behavior of the Fukaya category under the addition of a polynomial of type D.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Algebra and Geometry · Homotopy and Cohomology in Algebraic Topology