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
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author Pertusi, Laura
Stellari, Paolo
author_facet Pertusi, Laura
Stellari, Paolo
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description 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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spelling pubmed-103268952023-07-08 Categorical Torelli theorems: results and open problems Pertusi, Laura Stellari, Paolo Rend Circ Mat Palermo Article 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. Springer International Publishing 2022-09-15 2023 /pmc/articles/PMC10326895/ /pubmed/37425337 http://dx.doi.org/10.1007/s12215-022-00796-x Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article's Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article's Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Pertusi, Laura
Stellari, Paolo
Categorical Torelli theorems: results and open problems
title Categorical Torelli theorems: results and open problems
title_full Categorical Torelli theorems: results and open problems
title_fullStr Categorical Torelli theorems: results and open problems
title_full_unstemmed Categorical Torelli theorems: results and open problems
title_short Categorical Torelli theorems: results and open problems
title_sort categorical torelli theorems: results and open problems
topic Article
url 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
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