{"title":"DK conjecture for some K-inequivalences from Grassmannians","authors":"Naichung Conan Leung , Ying Xie","doi":"10.1016/j.jpaa.2024.107831","DOIUrl":null,"url":null,"abstract":"<div><div>The DK conjecture of Bondal-Orlov <span><span>[1]</span></span> and Kawamata <span><span>[2]</span></span> states that there should be an embedding of bounded derived categories for any <em>K</em>-inequivalence, which is proved to be true for the toroidal case (<span><span>[3]</span></span>, <span><span>[4]</span></span>, <span><span>[5]</span></span> and <span><span>[6]</span></span>). In this paper, we construct examples of non-toroidal <em>K</em>-inequivalences from Grassmannians inspired by <span><span>[7]</span></span>, <span><span>[8]</span></span>, <span><span>[9]</span></span> and <span><span>[10]</span></span>, and we show that these <em>K</em>-inequivalences satisfy the DK conjecture.</div></div>","PeriodicalId":54770,"journal":{"name":"Journal of Pure and Applied Algebra","volume":"229 1","pages":"Article 107831"},"PeriodicalIF":0.7000,"publicationDate":"2024-10-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Pure and Applied Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0022404924002287","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The DK conjecture of Bondal-Orlov [1] and Kawamata [2] states that there should be an embedding of bounded derived categories for any K-inequivalence, which is proved to be true for the toroidal case ([3], [4], [5] and [6]). In this paper, we construct examples of non-toroidal K-inequivalences from Grassmannians inspired by [7], [8], [9] and [10], and we show that these K-inequivalences satisfy the DK conjecture.
期刊介绍：
The Journal of Pure and Applied Algebra concentrates on that part of algebra likely to be of general mathematical interest: algebraic results with immediate applications, and the development of algebraic theories of sufficiently general relevance to allow for future applications.
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