{"title":"Néron–Severi Lie Algebra, Autoequivalences of the Derived Category, and Monodromy","authors":"V. Lunts","doi":"10.17323/1609-4514-2022-22-4-705-739","DOIUrl":null,"url":null,"abstract":"This preprint supersedes the previous version, which was only about Kontsevich's conjecture on the relation between the monodromy of a family of (weakly) CY varieties and the action on cohomology of the group of autoequivalences of the derived category of varieties in the mirror dual family. Here we add another conjecture about the relation of the group of autoequivalence of the derived category of a CY variety and its Neron-Severi Lie algebra.","PeriodicalId":54736,"journal":{"name":"Moscow Mathematical Journal","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2020-09-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Moscow Mathematical Journal","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.17323/1609-4514-2022-22-4-705-739","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
This preprint supersedes the previous version, which was only about Kontsevich's conjecture on the relation between the monodromy of a family of (weakly) CY varieties and the action on cohomology of the group of autoequivalences of the derived category of varieties in the mirror dual family. Here we add another conjecture about the relation of the group of autoequivalence of the derived category of a CY variety and its Neron-Severi Lie algebra.
期刊介绍:
The Moscow Mathematical Journal (MMJ) is an international quarterly published (paper and electronic) by the Independent University of Moscow and the department of mathematics of the Higher School of Economics, and distributed by the American Mathematical Society. MMJ presents highest quality research and research-expository papers in mathematics from all over the world. Its purpose is to bring together different branches of our science and to achieve the broadest possible outlook on mathematics, characteristic of the Moscow mathematical school in general and of the Independent University of Moscow in particular.
An important specific trait of the journal is that it especially encourages research-expository papers, which must contain new important results and include detailed introductions, placing the achievements in the context of other studies and explaining the motivation behind the research. The aim is to make the articles — at least the formulation of the main results and their significance — understandable to a wide mathematical audience rather than to a narrow class of specialists.