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. - (2022). [Epub ahead of print] [10.1007/s12215-022-00796-x]

Categorical Torelli theorems: results and open problems

L. Pertusi;P. Stellari
2022

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.
Derived categories; Semiorthogonal decompositions; Torelli theorems
Settore MAT/03 - Geometria
15-set-2022
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/940127
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