Variation of the Gieseker and Uhlenbeck Compactifications
Abstract
In this article, we study the variation of the Gieseker and Uhlenbeck compactifications of the moduli spaces of Mumford-Takemoto stable vector bundles of rank 2 by changing polarizations. Some {\it canonical} rational morphisms among the Gieseker compactifications are proved to exist and their fibers are studied. As a consequence of studying the morphisms from the Gieseker compactifications to the Uhlebeck compactifications, we show that there is an everywhere-defined {\it canonical} algebraic map between two adjacent Uhlenbeck compactifications which restricts to the identity on some Zariski open subset.
- Publication:
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arXiv e-prints
- Pub Date:
- September 1994
- DOI:
- 10.48550/arXiv.alg-geom/9409003
- arXiv:
- arXiv:alg-geom/9409003
- Bibcode:
- 1994alg.geom..9003H
- Keywords:
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- Mathematics - Algebraic Geometry
- E-Print:
- 24 pages, AmsLaTex