On the lie algebroid of a derived self-intersection

Abstract

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. © 2014 Elsevier Inc.