论文标题
关于马克曼问题的注释
A note on a question of Markman
论文作者
论文摘要
令$ \ Mathcal {f} $为复杂的投影代数$ x $上的矢量捆绑包。如果$ \ MATHCAL {F} $沿$ x $的一阶变形变形，则其Mukai Vector沿此变形沿Hodge类型保留。我们证明了所有polyvector字段的类似语句，不仅对$ h^1（x，t_x）$中的那些对应于复杂结构的变形。这回答了马克曼的问题。我们还探讨了上述陈述的理论类似物。
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.
