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Monads for framed torsion-free sheaves on multi-blow-ups of the projective plane. (English) Zbl 1330.14016
The author construct monads for framed torsion-free sheaves on blow-ups of the complex projective plane at finitely distinct points and then uses these monads to construct moduli spaces of these sheaves of a fixed Chern character. This is done by generalizing Buchdahl’s construction for vector bundles; see N. Buchdahl [Rocky Mt. J. Math. 34, No. 2, 513–540 (2004; Zbl 1061.14039)]. One proves that this moduli space is a smooth algebraic variety. Then one gives the construction of a monad corresponding to a flat family parametrized by a noetherian scheme of finite type and one ontains that the moduli space is fine. For another way of treating this moduli space see the papers: D. Huybrechts and M. Lehn [Int. J. Math. 6, No. 2, 297–324 (1995; Zbl 0865.14004)], H. Nakajima and K. Yoshioka [Invent. Math. 162, No. 2, 313–355 (2005; Zbl 1100.14009)], U. Bruzzo and D. Markushevich [Doc. Math., J. DMV 16, 399–410 (2011; Zbl 1222.14022)].

##### MSC:
 14D20 Algebraic moduli problems, moduli of vector bundles 14D21 Applications of vector bundles and moduli spaces in mathematical physics (twistor theory, instantons, quantum field theory) 14J60 Vector bundles on surfaces and higher-dimensional varieties, and their moduli