A note on a question of Markman

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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.
Original languageEnglish
Article number106673
Number of pages8
JournalJournal of Pure and Applied Algebra
Issue number9
Early online date7 Jan 2021
Publication statusPublished - Sept 2021


  • Hochschild homology and cohomology
  • HKR isomorphisms
  • Deformation


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