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Bubble tree compactification of moduli spaces of vector bundles on surfaces

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Markushevich D., Tikhomirov A., Trautmann G.

Open Mathematics

2012

tom 10

nr 4

1331-1355

We announce some results on compactifying moduli spaces of rank 2 vector bundles on surfaces by spaces of vector bundles on trees of surfaces. This is thought as an algebraic counterpart of the so-called bubbling of vector bundles and connections in differential geometry. The new moduli spaces are algebraic spaces arising as quotients by group actions according 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 1 = 2 on the projective plane is studied in more detail. Proofs are only indicated and will appear in separate papers.

Ograniczanie wyników

1 Open Mathematics

1 Markushevich D.

1 Tikhomirov A.

1 Trautmann G.

1 2012

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Bubble tree compactification of moduli spaces of vector bundles on surfaces