Dolbeault dga and L_∞-algebroid of the formal neighborhood

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• 作者：Shilin Yu ^{slyu@ims.cuhk.edu.hk" class="auth_mail" title="E-mail the corresponding author}
• 关键词：primary ; 14B20 ; secondary ; 16E45 ; 58A20
• 刊名：Advances in Mathematics
• 出版年：2017
• 出版时间：10 January 2017
• 年：2017
• 卷：305
• 期：Complete
• 页码：1131-1162
• 全文大小：523 K

文摘

We continue the study the Dolbeault dga of the formal neighborhood of an arbitrary closed embedding of complex manifolds previously defined by the author in [14]. The special case of the diagonal embedding has been analyzed in [13]. We describe here the Dolbeault dga of a general embedding explicitly in terms of the formal differential geometry of the embedding. Moreover, we show that the Dolbeault dga is the completed Chevalley–Eilenberg dga of an class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S000187081530205X&_mathId=si1.gif&_user=111111111&_pii=S000187081530205X&_rdoc=1&_issn=00018708&md5=4bf240b64aa94fe85c10534ea88dd33c" title="Click to view the MathML source">L_∞class="mathContainer hidden">class="mathCode">$L_{\infty }$-algebroid structure on the shifted normal bundle of the submanifold. This generalizes the result of Kapranov on the diagonal embedding and Atiyah class.