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 cat- egory of coherent sheaves of such a variety. The focus is on Enriques surfaces, prime Fano threefolds and cubic fourfolds.
Categorical Torelli theorems: results and open problems / L. Pertusi, P. Stellari. - In: RENDICONTI DEL CIRCOLO MATEMATICO DI PALERMO. - ISSN 1973-4409. - 72:(2023 Aug), pp. 2949-3011. [10.1007/s12215-022-00796-x]
Categorical Torelli theorems: results and open problems
L. PertusiPrimo
;P. Stellari
Ultimo
2023
Abstract
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 cat- egory of coherent sheaves of such a variety. The focus is on Enriques surfaces, prime Fano threefolds and cubic fourfolds.
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