{"title":"BPS invariants of symplectic log Calabi-Yau fourfolds","authors":"Mohammad Farajzadeh-Tehrani","doi":"10.1090/tran/9114","DOIUrl":null,"url":null,"abstract":"<p>Using the Fredholm setup of Farajzadeh-Tehrani [Peking Math. J. (2023), https://doi.org/10.1007/s42543-023-00069-1], we study genus zero (and higher) relative Gromov-Witten invariants with maximum tangency of symplectic log Calabi-Yau fourfolds. In particular, we give a short proof of Gross [Duke Math. J. 153 (2010), pp. 297–362, Cnj. 6.2] that expresses these invariants in terms of certain integral invariants by considering generic almost complex structures to obtain a geometric count. We also revisit the localization calculation of the multiple-cover contributions in Gross [Prp. 6.1] and recalculate a few terms differently to provide more details and illustrate the computation of deformation/obstruction spaces for maps that have components in a destabilizing (or rubber) component of the target. Finally, we study a higher genus version of these invariants and explain a decomposition of genus one invariants into different contributions.</p>","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2024-01-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1090/tran/9114","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0
Abstract
Using the Fredholm setup of Farajzadeh-Tehrani [Peking Math. J. (2023), https://doi.org/10.1007/s42543-023-00069-1], we study genus zero (and higher) relative Gromov-Witten invariants with maximum tangency of symplectic log Calabi-Yau fourfolds. In particular, we give a short proof of Gross [Duke Math. J. 153 (2010), pp. 297–362, Cnj. 6.2] that expresses these invariants in terms of certain integral invariants by considering generic almost complex structures to obtain a geometric count. We also revisit the localization calculation of the multiple-cover contributions in Gross [Prp. 6.1] and recalculate a few terms differently to provide more details and illustrate the computation of deformation/obstruction spaces for maps that have components in a destabilizing (or rubber) component of the target. Finally, we study a higher genus version of these invariants and explain a decomposition of genus one invariants into different contributions.
期刊介绍：
Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance.
Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.
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