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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