Serre algebra, matrix factorization and categorical Torelli theorem for hypersurfaces
X Lin, S Zhang - Mathematische Annalen, 2024 - Springer
Let X be a smooth Fano variety. We attach a bi-graded associative algebra HS (K u (X))=⨁ i,
j∈ Z Hom (Id, SK u (X) i [j]) to the Kuznetsov component K u (X) whenever it is defined. Then …
j∈ Z Hom (Id, SK u (X) i [j]) to the Kuznetsov component K u (X) whenever it is defined. Then …
Categorical cones and quadratic homological projective duality
A Kuznetsov, A Perry - arXiv preprint arXiv:1902.09824, 2019 - arxiv.org
We introduce the notion of a categorical cone, which provides a categorification of the
classical cone over a projective variety, and use our work on categorical joins to describe its …
classical cone over a projective variety, and use our work on categorical joins to describe its …
Periodic trivial extension algebras and fractionally Calabi-Yau algebras
A Chan, E Darpö, O Iyama, R Marczinzik - arXiv preprint arXiv:2012.11927, 2020 - arxiv.org
We study periodicity and twisted periodicity of the trivial extension algebra $ T (A) $ of a finite-
dimensional algebra $ A $. Our main results show that (twisted) periodicity of $ T (A) $ is …
dimensional algebra $ A $. Our main results show that (twisted) periodicity of $ T (A) $ is …
Derived factorization categories of non‐Thom–Sebastiani‐type sums of potentials
Y Hirano, G Ouchi - Proceedings of the London Mathematical …, 2023 - Wiley Online Library
We first prove semi‐orthogonal decompositions of derived factorization categories arising
from sums of potentials of gauged Landau–Ginzburg models, where the sums are not …
from sums of potentials of gauged Landau–Ginzburg models, where the sums are not …
Toric Exoflops and Categorical Resolutions
TL Kelly, A Malter - arXiv preprint arXiv:2407.19822, 2024 - arxiv.org
We study the exoflop introduced by Aspinwall. Here, an exoflop takes a gauged Landau-
Ginzburg (LG) model, partially compactifies it, and then performs certain birational …
Ginzburg (LG) model, partially compactifies it, and then performs certain birational …
Exceptional collections for mirrors of invertible polynomials
We prove the existence of a full exceptional collection for the derived category of equivariant
matrix factorizations of an invertible polynomial with its maximal symmetry group. This …
matrix factorizations of an invertible polynomial with its maximal symmetry group. This …
IVHS via Kuznetsov components and categorical Torelli theorems for weighted hypersurfaces
X Lin, JV Rennemo, S Zhang - arXiv preprint arXiv:2408.08266, 2024 - arxiv.org
We study the categorical Torelli theorem for smooth (weighted) hypersurfaces in (weighted)
projective spaces via the Hochschild--Serre algebra of its Kuznetsov component. In the first …
projective spaces via the Hochschild--Serre algebra of its Kuznetsov component. In the first …
Topological K-theory of quasi-BPS categories of symmetric quivers with potential
T Pădurariu, Y Toda - arXiv preprint arXiv:2309.08432, 2023 - arxiv.org
In previous work, we studied quasi-BPS categories (of symmetric quivers with potential, of
preprojective algebras, of surfaces) and showed they have properties analogous to those of …
preprojective algebras, of surfaces) and showed they have properties analogous to those of …
Quasi-BPS categories for K3 surfaces
T Pădurariu, Y Toda - arXiv preprint arXiv:2309.08437, 2023 - arxiv.org
We introduce and begin the study of quasi-BPS categories for K3 surfaces, which are a
categorical version of the BPS cohomologies for K3 surfaces. We construct semiorthogonal …
categorical version of the BPS cohomologies for K3 surfaces. We construct semiorthogonal …
Kuznetsov's Fano threefold conjecture via Hochschild–Serre algebra
X Lin, S Zhang - Mathematische Zeitschrift, 2024 - Springer
Let Y be a smooth quartic double solid regarded as a degree 4 hypersurface of the weighted
projective space P (1, 1, 1, 1, 2). We study the multiplication of the Hochschild-Serre algebra …
projective space P (1, 1, 1, 1, 2). We study the multiplication of the Hochschild-Serre algebra …