Categorical Torelli theorems: results and open problems
L Pertusi, P Stellari - Rendiconti del Circolo Matematico di Palermo Series …, 2023 - Springer
We survey some recent results concerning the so called Categorical Torelli problem. This is
to say how one can reconstruct a smooth projective variety up to isomorphism, by using the …
to say how one can reconstruct a smooth projective variety up to isomorphism, by using the …
Categorical Torelli theorems for Gushel–Mukai threefolds
A Jacovskis, X Lin, Z Liu… - Journal of the London …, 2024 - Wiley Online Library
We show that a general ordinary Gushel–Mukai (GM) threefold XX can be reconstructed
from its Kuznetsov component K u (X) Ku(X) together with an extra piece of data coming from …
from its Kuznetsov component K u (X) Ku(X) together with an extra piece of data coming from …
[PDF][PDF] Moduli spaces on the Kuznetsov component of Fano threefolds of index 2
M Altavilla, M Petkovic, F Rota - Épijournal de Géométrie …, 2022 - epiga.episciences.org
General hyperplane sections of a Fano threefold Y of index 2 and Picard rank 1 are del
Pezzo surfaces, and their Picard group is related to a root system. To the corresponding …
Pezzo surfaces, and their Picard group is related to a root system. To the corresponding …
A computational view on the non-degeneracy invariant for Enriques surfaces
R Moschetti, F Rota, L Schaffler - Experimental Mathematics, 2024 - Taylor & Francis
For an Enriques surface S, the non-degeneracy invariant nd (S) retains information on the
elliptic fibrations of S and its polarizations. In the current paper, we introduce a combinatorial …
elliptic fibrations of S and its polarizations. In the current paper, we introduce a combinatorial …
Three approaches to a categorical Torelli theorem for cubic threefolds of non-Eckardt type via the equivariant Kuznetsov components
S Casalaina-Martin, X Hu, X Lin, S Zhang… - arXiv preprint arXiv …, 2024 - arxiv.org
Let $ Y $ be a cubic threefold with a non-Eckardt type involution $\tau $. Our first main result
is that the $\tau $-equivariant category of the Kuznetsov component $\mathcal {K} u …
is that the $\tau $-equivariant category of the Kuznetsov component $\mathcal {K} u …
Categorical Torelli theorems for Fano threefolds
A Jacovskis - 2024 - era.ed.ac.uk
The derived category Db (X) of a variety contains a lot of information about X. If X and X′
are Fano, then an equivalence Db (X)≃ Db (X′) implies that X and X′ are isomorphic. For …
are Fano, then an equivalence Db (X)≃ Db (X′) implies that X and X′ are isomorphic. For …