The Hochschild-Kostant-Rosenberg isomorphism for quantized analytic cycles

Abstract

In this article, we provide a detailed account of a construction sketched by Kashiwara in an unpublished manuscript concerning generalized HKR isomorphisms for smooth analytic cycles whose conormal exact sequence splits. It enables us, among other applications, to solve a problem raised recently by Arinkin and Căldăraru about uniqueness of such HKR isomorphisms in the case of the diagonal injection. Using this construction, we also associate with any smooth analytic cycle endowed with an infinitesimal retraction a cycle class which is an obstruction for the cycle to be the vanishing locus of a transverse section of a holomorphic vector bundle.

Mistake corrected in Section 5.2

References in corpus (2)

• The relative Riemann-Roch theorem from Hochschild homology
• A variant of the Mukai pairing via deformation quantization

Cited by in corpus (5)

• Formality of derived intersections
• Derived geometry of the first formal neighborhood of a smooth analytic cycle
• The Ext algebra of a quantized cycle
• Dolbeault dga and $L_{\infty }$-algebroid of the formal neighborhood
• Modèles géométriques attachés aux paires réductives