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.
- Hochschild homology and cohomology
- HKR isomorphisms