Uhlenbeck-Donaldson compactification for framed sheaves on projective surfaces

被引：5

作者：

Bruzzo, Ugo ^{[1
,2
]}

Markushevich, Dimitri ^{[3
]}

Tikhomirov, Alexander ^{[4
]}

机构：

[1] Scuola Int Sup Avanzati, I-34136 Trieste, Italy

[2] Ist Nazl Fis Nucl, Sez Trieste, I-34136 Trieste, Italy

[3] Univ Lille 1, F-59655 Villeneuve Dascq, France

[4] Yaroslavl State Pedag Univ, Dept Math, Yaroslavl 150000, Russia

来源：

MATHEMATISCHE ZEITSCHRIFT | 2013年 / 275卷 / 3-4期

关键词：

Framed sheaves; Moduli spaces; Uhlenbeck-Donaldson compactification; Stable pairs; Instantons; STABLE SHEAVES; REPRESENTATIONS; RESTRICTION; MODULI;

D O I：

10.1007/s00209-013-1170-9

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We construct a compactification of the Uhlenbeck-Donaldson type for the moduli space of slope stable framed bundles. This is a kind of a moduli space of slope semistable framed sheaves. We show that there exists a projective morphism , where is the moduli space of S-equivalence classes of Gieseker-semistable framed sheaves. The space has a natural set-theoretic stratification which allows one, via a Hitchin-Kobayashi correspondence, to compare it with the moduli spaces of framed ideal instantons.

引用

页码：1073 / 1093

页数：21

共 17 条

[1] Uhlenbeck–Donaldson compactification for framed sheaves on projective surfaces
Ugo Bruzzo
Dimitri Markushevich
Alexander Tikhomirov
Mathematische Zeitschrift, 2013, 275 : 1073 - 1093
[2] MODULI OF FRAMED SHEAVES ON PROJECTIVE SURFACES
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Markushevish, Dimitri
DOCUMENTA MATHEMATICA, 2011, 16 : 399 - 410
[3] Framed sheaves on projective stacks
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[4] Parabolic bundles on algebraic surfaces I - The Donaldson-Uhlenbeck compactification
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PROCEEDINGS OF THE INDIAN ACADEMY OF SCIENCES-MATHEMATICAL SCIENCES, 2008, 118 (01): : 43 - 79
[5] Parabolic bundles on algebraic surfaces I — The Donaldson-Uhlenbeck compactification
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[6] Framed symplectic sheaves on surfaces
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[7] Symplectic structures on moduli spaces of framed sheaves on surfaces
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[8] Moduli spaces of framed flags of sheaves on the projective plane
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[9] MONADS FOR FRAMED TORSION-FREE SHEAVES ON MULTI-BLOW-UPS OF THE PROJECTIVE PLANE
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INTERNATIONAL JOURNAL OF MATHEMATICS, 2014, 25 (01)
[10] Framed sheaves on projective space and Quot schemes
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MATHEMATISCHE ZEITSCHRIFT, 2022, 300 (01) : 745 - 760

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