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arXiv · 2011.10207

A note on a question of Markman

Shengyuan Huang
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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.

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Shengyuan Huang. 2020-11-20. A note on a question of Markman. https://doi.org/10.1016/j.jpaa.2021.106673

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