Semistability of certain bundles on a quintic Calabi-Yau threefold (Q1009451)

The paper arises from a physical paper by \textit{M. R. Douglas} and \textit{C.-G. Zhou} [Chirality Change in String Theory, JHEP 0406, 014 (2004); cf. \url{arXiv:hep-th/0403018}], where the stability of some bundles on a quintic Calabi-Yau threefold is investigated. The paper proves the semistability of most bundles listed and discussed by Douglas and Zhou. It comes out that rank \(3\), rank \(4\) and rank \(> 4\) must be investigated with different methods. In particular the rank \(> 4\) case makes use of the stability theorems on \(\mathbb{P}^2\) proved by \textit{J. M. Drèzet} and \textit{J. Le Potier} [Ann. Sci. Ècole Norm. Supér., 18, 193--243 (1985; Zbl 0586.14007)].