On the Lie algebroid of a derived self-intersection

Abstract

Let $i:X\hookrightarrow Y$ be a closed embedding of smooth algebraic varieties. Denote by $N$ the normal bundle of $X$ in $Y$. We describe the construction of two Lie-type structures on the shifted bundle $N[-1]$ which encode the information of the formal neighborhood of $X$ inside $Y$. We also present applications of classical Lie theoretic constructions (universal enveloping algebra, Chevalley-Eilenberg complex) to the understanding of the geometry of embeddings.

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References in corpus (1)

• Derived Algebraic Geometry V: Structured Spaces

Cited by in corpus (7)

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• A categorification of the quantum Lefschetz principle
• Modèles géométriques attachés aux paires réductives