Boundedness of semi-stable sheaves of small ranks
- 1 May 1980
- journal article
- research article
- Published by Cambridge University Press (CUP) in Nagoya Mathematical Journal
- Vol. 78, 65-94
- https://doi.org/10.1017/s002776300001881x
Abstract
As for the construction of moduli spaces of stable sheaves, the boundedness of semi-stable sheaves is one of the most important questions which are left unanswered. In the case of dimension one, the boundedness was proved by M. F. Atiyah [1]. When the dimension of the base variety is two and the rank is two, F. Takemoto and D. Mumford showed the boundedness independently ([13]). The author proved in [7] that the boundedness holds for every rank in the case of dimension two, and then D. Gieseker gave another proof of it in [3].Keywords
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