The Hochschild-Kostant-Rosenberg Isomorphism for Quantized Analytic Cycles

Julien Grivaux (1, 2)

1 LATP - Laboratoire d'Analyse, Topologie, Probabilités
2 INSMI-CNRS - Institut National des Sciences Mathématiques et de leurs Interactions - CNRS Mathématiques

In this article, we provide a detailed account of a construction sketched by Kashiwara in an unpublished manuscript concerning generalized HKR isomorphisms for smooth analytic cycles whose conormal exact sequence splits.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 C\u{a}ld\u{a}raru 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.

Mots clés: Hochschild-Kostant-Rosenberg isomorphism; conjecture of Kashiwara; holomorphic vector bundle

Domaines: Géométrie algébrique [math.AG]

Julien Grivaux. The Hochschild-Kostant-Rosenberg Isomorphism for Quantized Analytic Cycles. International Mathematics Research Notices, 2014, 2014 (4), pp.865--913. ⟨10.1093/imrn/rns238⟩. ⟨hal-01301438⟩