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

Dimitri Markushevich; Alexander Tikhomirov; Günther Trautmann

Open Mathematics (2012)

- Volume: 10, Issue: 4, page 1331-1355
- ISSN: 2391-5455

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topDimitri Markushevich, Alexander Tikhomirov, and Günther Trautmann. "Bubble tree compactification of moduli spaces of vector bundles on surfaces." Open Mathematics 10.4 (2012): 1331-1355. <http://eudml.org/doc/269293>.

@article{DimitriMarkushevich2012,

abstract = {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.},

author = {Dimitri Markushevich, Alexander Tikhomirov, Günther Trautmann},

journal = {Open Mathematics},

keywords = {Instantons; Vector bundles; Coherent sheaves; Moduli spaces of sheaves; Donaldson-Uhlenbeck compactification; Monads; Serre construction; Fulton-McPherson compactification; instantons; vector bundles; coherent sheaves; moduli spaces of sheaves; monads},

language = {eng},

number = {4},

pages = {1331-1355},

title = {Bubble tree compactification of moduli spaces of vector bundles on surfaces},

url = {http://eudml.org/doc/269293},

volume = {10},

year = {2012},

}

TY - JOUR

AU - Dimitri Markushevich

AU - Alexander Tikhomirov

AU - Günther Trautmann

TI - Bubble tree compactification of moduli spaces of vector bundles on surfaces

JO - Open Mathematics

PY - 2012

VL - 10

IS - 4

SP - 1331

EP - 1355

AB - 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.

LA - eng

KW - Instantons; Vector bundles; Coherent sheaves; Moduli spaces of sheaves; Donaldson-Uhlenbeck compactification; Monads; Serre construction; Fulton-McPherson compactification; instantons; vector bundles; coherent sheaves; moduli spaces of sheaves; monads

UR - http://eudml.org/doc/269293

ER -

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