Abstract We introduce the notion of Hitchin variety over C . Let L be a holomorphic line bundle over a Hitchin variety X. We investigate the space of all global sections of sheaf of differential operators D k ( L ) and symmetric powers of sheaf of first order differential operators S k ( D 1 ( L ) ) over X and show that for a projective Hithcin variety both the spaces are one dimensional. As an application, we show that the space C ( L ) of holomorphic connections on L does not admit any non-constant regular function.

中文翻译：

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Hitchin 变数的微分算子

摘要 我们在 C 上引入了 Hitchin 变体的概念。设 L 是 Hitchin 簇 X 上的全纯线丛。我们研究了微分算子 D k ( L ) 和一阶微分算子 S k ( D 1 ( L ) ) 层的对称幂的所有全局截面的空间在 X 上并证明对于射影 Hithcin 变体，两个空间都是一维的。作为一个应用，我们证明了 L 上全纯连接的空间 C ( L ) 不允许任何非常数正则函数。