Categorical Torelli theorems: results and open problems

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 homological properties of special admissible subcategories of the bounded derived category of coherent sheaves of suc...

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Detalles Bibliográficos
Autores principales: Pertusi, Laura, Stellari, Paolo
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer International Publishing 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10326895/
https://www.ncbi.nlm.nih.gov/pubmed/37425337
http://dx.doi.org/10.1007/s12215-022-00796-x
Descripción
Sumario: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 homological properties of special admissible subcategories of the bounded derived category of coherent sheaves of such a variety. The focus is on Enriques surfaces, prime Fano threefolds and cubic fourfolds.

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