{"title":"Invariant stability conditions of local P1×P1 (after Del Monte-Longhi)","authors":"Yirui Xiong","doi":"10.1016/j.jalgebra.2025.03.005","DOIUrl":null,"url":null,"abstract":"<div><div>Let <em>X</em> be the total space of the canonical bundle of <span><math><msup><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msup><mo>×</mo><msup><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>, we study an invariant subspace of stability conditions on <em>X</em> under an autoequivalence of <span><math><msup><mrow><mi>D</mi></mrow><mrow><mi>b</mi></mrow></msup><mo>(</mo><mi>X</mi><mo>)</mo></math></span>. We describe the complete set of stable objects with respect to the invariant stability conditions and characterize the space of invariant stability conditions.</div></div>","PeriodicalId":14888,"journal":{"name":"Journal of Algebra","volume":"671 ","pages":"Pages 189-234"},"PeriodicalIF":0.8000,"publicationDate":"2025-03-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Algebra","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0021869325001188","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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Abstract
Let X be the total space of the canonical bundle of , we study an invariant subspace of stability conditions on X under an autoequivalence of . We describe the complete set of stable objects with respect to the invariant stability conditions and characterize the space of invariant stability conditions.
期刊介绍：
The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.
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