A note on a question of Markman
Abstract
Let $\mathcal{F}$ be a vector bundle on a complex projective algebraic variety $X$. If $\mathcal{F}$ 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 $H^1(X,T_X)$ corresponding to deformations of the complex structure. This answers a question of Markman. We also explore a Lie theoretic analogue of the statement above.
- Publication:
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arXiv e-prints
- Pub Date:
- November 2020
- DOI:
- 10.48550/arXiv.2011.10207
- arXiv:
- arXiv:2011.10207
- Bibcode:
- 2020arXiv201110207H
- Keywords:
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- Mathematics - Algebraic Geometry;
- 14F06;
- 16E40
- E-Print:
- Final version, 10 pages