Hilbert polynomials of moduli spaces of rank 2 vector bundles. II
[For part I see \textit{A. Szenes}, ibid. 587-597 (1993; see the preceding review).] Let \({\mathcal M}^ C_ 0\) be the moduli space of semi-stable rank 2 vector bundles with fixed even degree determinant on a curve \(C\), and denote by \(L_ 0\) the generator of \(\text{Pic} {\mathcal M}^ C_ 0\). The authors prove the following formula \[ \dim H^ 0 ({\mathcal M}^ C_ 0, L_ 0^{k-2}) = \sum^{k-1}_{J = +} (k/1 - \cos 2j \pi/k)^{g-1}. \] To prove this formula the authors use the Hecke correspondence between the two moduli spaces \({\mathcal M}^ C_ 0\) and \({\mathcal M}^ C_ 1\) to transfer the calculation from \({\mathcal M}^ C_ 0\) to \({\mathcal M}^ C_ 1\).
moduli space of semi-stable rank 2 vector
scientific article; zbMATH DE number 488117