Given a compact Riemann surface X of genus at least 2 with automorphism group G, we provide formulae that enable us to compute traces of automorphisms of X on the space of global sections of G-linearized line bundles defined on certain blow-ups of projective spaces along the curve X. The method is an adaptation of one used by Thaddeus to compute the dimensions of those spaces. In particular, we can compute the traces of automorphisms of X on the Verlinde spaces corresponding to the moduli space \(SU_{X}(2,\xi )\) when \(\xi \) is a line bundle G-linearized of suitable degree.

中文翻译：

---

$$SU_{X}(2,\xi )$$ 和放大的 Verlinde 迹线

给定亏格至少为 2 且具有自同构群G的紧黎曼曲面X，我们提供的公式使我们能够计算X在G线性化线束的全局截面空间上的自同构迹，这些线束定义在投影空间的某些放大上沿着曲线X。该方法是对 Thaddeus 用来计算这些空间维度的方法的改编。特别地，当\(\xi \)是线丛G线性化时，我们可以计算对应于模空间\(SU_{X}(2,\xi )\) 的Verlinde 空间上X的自同构迹合适的程度。