范畴Torelli定理：结果和开放问题。

Pub Date : 2023-01-01 Epub Date: 2022-09-15 DOI:10.1007/s12215-022-00796-x

Laura Pertusi, Paolo Stellari

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引用次数: 10

摘要

我们调查了最近关于所谓的分类Torelli问题的一些结果。这就是说，如何通过利用光滑射影变种的相干簇的有界派生范畴的特殊可容许子范畴的同调性质，重建光滑射影变种直至同构。重点是Enriques曲面，素数Fano三重和立方四重。

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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 such a variety. The focus is on Enriques surfaces, prime Fano threefolds and cubic fourfolds.

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