A note on a question of Markman

Shengyuan Huang

doi:10.1016/j.jpaa.2021.106673

A note on a question of Markman

Shengyuan Huang

Mathematics

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Abstract

Let ℱ be a vector bundle on a complex projective algebraic variety X. If ℱ deforms along a first order deformation of X, its Mukai vector remains of Hodge type along this deformation. We prove an analogous statement for all polyvector fields, not only for those in H¹ (X, T_x) corresponding to deformations of the complex structure. This answers a question of Markman. We also explore a Lie theoretic analogue of the statement above.

Original language	English
Article number	106673
Number of pages	8
Journal	Journal of Pure and Applied Algebra
Volume	225
Issue number	9
Early online date	7 Jan 2021
DOIs	https://doi.org/10.1016/j.jpaa.2021.106673
Publication status	Published - Sept 2021

Keywords

Hochschild homology and cohomology
HKR isomorphisms
Deformation

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AB - Let ℱ be a vector bundle on a complex projective algebraic variety X. If ℱ deforms along a first order deformation of X, its Mukai vector remains of Hodge type along this deformation. We prove an analogous statement for all polyvector fields, not only for those in H1 (X, Tx) corresponding to deformations of the complex structure. This answers a question of Markman. We also explore a Lie theoretic analogue of the statement above.

KW - Hochschild homology and cohomology

KW - HKR isomorphisms

KW - Deformation

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DO - 10.1016/j.jpaa.2021.106673

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JF - Journal of Pure and Applied Algebra

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A note on a question of Markman

Abstract

Keywords

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