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arXiv · 1306.5260

On the Lie algebroid of a derived self-intersection

Damien Calaque·Andrei Caldararu·Junwu Tu
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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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Damien Calaque, Andrei Caldararu, Junwu Tu. 2014-06-29. On the Lie algebroid of a derived self-intersection. https://doi.org/10.1016/j.aim.2014.06.002

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