2018/06/12 by Yankı Lekili, Lekili, Yanki, Kazushi Ueda +1
Mathematics · #Advanced Combinatorial Mathematics #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT) #Symplectic Geometry (math.SG)
paper · pdf · doi:10.48550/arxiv.1806.04345
openalex publication_date 2018/06/12 · openalex created_date 2022/09/06 · openalex updated_date 2026/07/28
We show that the base spaces of the semiuniversal unfoldings of some weighted homogeneous singularities can be identified with moduli spaces of A_∞-structures on the trivial extension algebras of the endomorphism algebras of the tilting objects. The same algebras also appear in the Fukaya categories of their mirrors. Based on these identifications, we discuss applications to homological mirror symmetry for Milnor fibers, and give a proof of homological mirror symmetry for an n-dimensional affine hypersurface of degree n + 2 and the double cover of the n-dimensional affine space branched along a degree 2n + 2 hypersurface. Along the way, we also give a proof of a conjecture of Seidel from math/0206155 which may be of independent interest.