[图书][B] Representation theory of Geigle-Lenzing complete intersections

M Herschend, O Iyama, H Minamoto, S Oppermann - 2023 - ams.org
Weighted projective lines, introduced by Geigle and Lenzing in 1987, are important objects
in representation theory. They have tilting bundles, whose endomorphism algebras are the …

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 Milnor fibers of simple singularities

Y Lekili, K Ueda - arXiv preprint arXiv:2004.07374, 2020 - arxiv.org
We prove homological mirror symmetry for Milnor fibers of simple singularities in dimensions
greater than one, which are among the log Fano cases of Conjecture 1.5 in arXiv …

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 …

Orlov's theorem for dg-algebras

MK Brown, P Sridhar - Advances in Mathematics, 2025 - Elsevier
A landmark theorem of Orlov relates the singularity category of a graded Gorenstein algebra
to the derived category of the associated noncommutative projective scheme. We generalize …

Recent progress on SYZ mirror symmetry for some non-compact Calabi-Yau surfaces

TC Collins, YS Lin - arXiv preprint arXiv:2208.14485, 2022 - arxiv.org
We survey the authors recent works, joint with A. Jacob, on Strominger-Yau-Zaslow mirror
symmetry for rational elliptic surfaces and del Pezzo surfaces. We discuss some …

Homological Berglund-H\" ubsch mirror symmetry for curve singularities

M Habermann, J Smith - arXiv preprint arXiv:1903.01351, 2019 - arxiv.org
Given a two-variable invertible polynomial, we show that its category of maximally-graded
matrix factorisations is quasi-equivalent to the Fukaya-Seidel category of its Berglund-H\" …

Suspending Lefschetz fibrations, with an application to local mirror symmetry

P Seidel - Communications in Mathematical Physics, 2010 - Springer
We describe the behaviour of Fukaya categories under “suspension”, which means passing
from the fibre of a Lefschetz fibration to the double cover of the total space branched along …

Tilting Cohen–Macaulay representations

O Iyama - Proceedings of the International Congress of …, 2018 - World Scientific
Proceedings of the International Congress of Mathematicians (ICM 2018) : TILTING COHEN–MACAULAY
REPRESENTATIONS Page 1 P . I . C . M . – 2018 Rio de Janeiro, Vol. 2 (125–162) TILTING …

Enhanced Auslander-Reiten duality and tilting theory for singularity categories

N Hanihara, O Iyama - arXiv preprint arXiv:2209.14090, 2022 - arxiv.org
We establish a general method to construct triangle equivalences between the singularity
categories of (commutative and non-commutative) Gorenstein rings and the cluster …