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$%M. C. Brambilla, Semistability of certain bon a quintic Calabi-Yau threefold, Rev. Mat. Complut. 22 (2009), no. 1, 53–61.%$
In a recent paper Douglas and Zhou aim for explicit examples of string theory compactifications that have a different number of generations and can be connected. For this purpose, they provide a list of bundles on a quintic Calabi-Yau threefold. They need to show that (at least some of) these bundles are semistable and leave this as an open question. In this paper we prove the semistability of most of the bundles in the list, thus completing the result of Douglas and Zhou.
Key words: semistability, vector bundles.
2000 Mathematics Subject Classification: 14J60, 14F05.