On the Lie algebroid of a derived self-intersection

Let i:X↪Y be a closed embedding of smooth algebraic varieties. Denote by N the normal bundle of X in Y. The present paper contains two constructions of certain Lie structure on the shifted normal bundle N[−1] encoding the information of the formal neighborhood of X in Y. We also present a few applic...

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Bibliographic Details
Published inAdvances in mathematics (New York. 1965) Vol. 262; pp. 751 - 783
Main Authors Calaque, Damien, Căldăraru, Andrei, Tu, Junwu
Format Journal Article
LanguageEnglish
Published Elsevier Inc 10.09.2014
Elsevier
Subjects
Algebraic Geometry
Deformation
Embedding
Lie algebroid
Mathematics
Quantum Algebra
Embedding
Deformation
Lie algebroid
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Summary:Let i:X↪Y be a closed embedding of smooth algebraic varieties. Denote by N the normal bundle of X in Y. The present paper contains two constructions of certain Lie structure on the shifted normal bundle N[−1] encoding the information of the formal neighborhood of X in Y. We also present a few applications of these Lie theoretic constructions in understanding the algebraic geometry of embeddings.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2014.06.002