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## Bubble tree compactification of moduli spaces of vector bundles on surfaces

Central European Journal of Mathematics. 2012. Vol. 19. No. 4. P. 1331-1355.
Tikhomirov A. S., Markushevich D., Trautmann G.
We announce some results on compactifying moduli spaces of rank 2 vector bundles on surfaces by spaces of vector vector bundles on trees of surfaces. This is thought as an algebraic counterpart of the so-called bubbling of vector bundled connections an in differential geometry. The new moduli spaces are algebraic spaces arising as quotients by group actions according surfaces to a result of Kollár. As an example, the compactification of the space of stable rank 2 vector bundles with Chern classes $c_1=0, c_2=2$ on the projective plane is studied in more detail. Proofs are only indicated and will appear in separate papers.