Variation of the Gieseker and Uhlenbeck Compactifications

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.