Categorical Torelli theorems: results and open problems.

IF 0.9 Q2 MATHEMATICS

Rendiconti del Circolo Matematico di Palermo Pub Date : 2023-01-01 Epub Date: 2022-09-15 DOI:10.1007/s12215-022-00796-x

Laura Pertusi, Paolo Stellari

引用次数: 10

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

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范畴Torelli定理：结果和开放问题。

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。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Rendiconti del Circolo Matematico di Palermo MATHEMATICS-

CiteScore

2.20

自引率

10.00%

发文量

138

期刊介绍： The Rendiconti del Circolo Matematico di Palermo is an international journal publishing original research papers on pure and applied mathematics, focusing in particular on: Algebra, Algebraic Geometry, Arithmetic Geometry and Number Theory, Calculus of Variations, Partial Differential Equations, Ordinary Differential Equations, Functional Analysis, Complex Analysis, and applications of the above fields. Submissions, since foundation of the journal, are refereed by an international editorial board of Mathematicians. Due to publishing constraints, only two submissions per author per year will be considered, at the discretion of the Editors-in-Chief.The Rendiconti del Circolo Matematico di Palermo is the Journal of the ''Circolo Matematico di Palermo'', a nonprofit organization, founded by Gian Battista Guccia in 1884. The publication of this journal is in two series: The first series, published between 1885 and 1941, consists of 63 volumes, and almost all of them are still available. The second series began in 1952 and, starting with volume 57 (2008), will be published in cooperation with Springer-Verlag.