Homological mirror symmetry for Milnor fibers via moduli of A∞ A_∞‐structures

Y Lekili, K Ueda - Journal of Topology, 2022 - Wiley Online Library
We show that the base spaces of the semiuniversal unfoldings of some weighted
homogeneous singularities can be identified with moduli spaces of A∞ A_∞‐structures on …

Homological mirror symmetry for Brieskorn–Pham singularities

M Futaki, K Ueda - Selecta Mathematica, 2011 - Springer
We prove that the derived Fukaya category of the Lefschetz fibration defined by a Brieskorn–
Pham polynomial is equivalent to the triangulated category of singularities associated with …

Localized mirror functor for Lagrangian immersions, and homological mirror symmetry for

CH Cho, H Hong, SC Lau - Journal of Differential Geometry, 2017 - projecteuclid.org
This paper gives a new way of constructing Landau–Ginzburg mirrors using deformation
theory of Lagrangian immersions motivated by the works of Seidel, Strominger–Yau–Zaslow …

Lagrangian tori in four-dimensional Milnor fibres

A Keating - Geometric and Functional Analysis, 2015 - Springer
The Milnor fibre of any isolated hypersurface singularity contains many exact Lagrangian
spheres: the vanishing cycles associated to a Morsification of the singularity. Moreover, for …

Triangulated categories of matrix factorizations for regular systems of weights with ε=− 1

H Kajiura, K Saito, A Takahashi - Advances in Mathematics, 2009 - Elsevier
We construct a full strongly exceptional collection in the triangulated category of graded
matrix factorizations of a polynomial associated to a nondegenerate regular system of …

Spectral analysis of finite dimensional algebras and singularities

H Lenzing, JA de la Pena - arXiv preprint arXiv:0805.1018, 2008 - arxiv.org
We give a summary on spectral techniques for finite dimensional algebras and study its link
to singularity theory. In particular, we offer a contribution to the categorification of the Milnor …

A note on entropy of auto-equivalences: lower bound and the case of orbifold projective lines

K Kikuta, Y Shiraishi, A Takahashi - Nagoya Mathematical Journal, 2020 - cambridge.org
Entropy of categorical dynamics is defined by Dimitrov–Haiden–Katzarkov–Kontsevich.
Motivated by the fundamental theorem of the topological entropy due to Gromov–Yomdin, it …

Inducing stability conditions

E Macri, S Mehrotra, P Stellari - arXiv preprint arXiv:0705.3752, 2007 - arxiv.org
We study stability conditions induced by functors between triangulated categories. Given a
finite group acting on a smooth projective variety we prove that the subset of invariant …

Extended canonical algebras and Fuchsian singularities

H Lenzing, JA de la Peña - Mathematische Zeitschrift, 2011 - Springer
The authors introduce a new class of finite dimensional algebras called extended canonical,
and determine the shape of their derived categories. Extended canonical algebras arise …

Homological mirror symmetry for Milnor fibers via moduli of -structures

Y Lekili, K Ueda - arXiv preprint arXiv:1806.04345, 2018 - arxiv.org
We show that the base spaces of the semiuniversal unfoldings of some weighted
homogeneous singularities can be identified with moduli spaces of $ A_\infty $-structures on …