{"title":"范畴Torelli定理：结果和开放问题。","authors":"Laura Pertusi, Paolo Stellari","doi":"10.1007/s12215-022-00796-x","DOIUrl":null,"url":null,"abstract":"<p><p>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.</p>","PeriodicalId":46620,"journal":{"name":"Rendiconti del Circolo Matematico di Palermo","volume":"72 5","pages":"2949-3011"},"PeriodicalIF":0.9000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10326895/pdf/","citationCount":"10","resultStr":"{\"title\":\"Categorical Torelli theorems: results and open problems.\",\"authors\":\"Laura Pertusi, Paolo Stellari\",\"doi\":\"10.1007/s12215-022-00796-x\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p><p>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.</p>\",\"PeriodicalId\":46620,\"journal\":{\"name\":\"Rendiconti del Circolo Matematico di Palermo\",\"volume\":\"72 5\",\"pages\":\"2949-3011\"},\"PeriodicalIF\":0.9000,\"publicationDate\":\"2023-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10326895/pdf/\",\"citationCount\":\"10\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Rendiconti del Circolo Matematico di Palermo\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1007/s12215-022-00796-x\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"2022/9/15 0:00:00\",\"PubModel\":\"Epub\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Rendiconti del Circolo Matematico di Palermo","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1007/s12215-022-00796-x","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2022/9/15 0:00:00","PubModel":"Epub","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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.
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.
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