×

zbMATH — the first resource for mathematics

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
PDF BibTeX XML Cite
Full Text: DOI arXiv
References:
[1] Ancona V., Atti Accad. Peloritana Pericolanti Cl. Sci. Fis. Mat. Natur. 67 pp 99–
[2] Ancona V., Forum Math. 3 pp 157–
[3] DOI: 10.1016/0375-9601(78)90141-X · Zbl 0424.14004 · doi:10.1016/0375-9601(78)90141-X
[4] DOI: 10.1007/978-3-642-96754-2 · doi:10.1007/978-3-642-96754-2
[5] Beauville A., Astérisque, in: Surfaces Algébriques Complexes (1978)
[6] DOI: 10.1216/rmjm/1181069865 · Zbl 1061.14039 · doi:10.1216/rmjm/1181069865
[7] Godement R., Topologie Algébrique et Théorie des Faisceaux (1958)
[8] Grothendieck A., Tohoku Math. J. 9 pp 119–
[9] Grothendieck A., Séminaires Claude Chevalley 3 pp 1–
[10] Grothendieck A., Publ. Math. Inst. Hautes Études Sci. 11 pp 5–
[11] Hartshorne R., Lecture Notes Mathematics 20, in: Residues and Duality (1966) · Zbl 0212.26101 · doi:10.1007/BFb0080482
[12] DOI: 10.1007/978-1-4757-3849-0 · doi:10.1007/978-1-4757-3849-0
[13] DOI: 10.1017/S0017089510000558 · Zbl 1238.14010 · doi:10.1017/S0017089510000558
[14] DOI: 10.1007/BF01450934 · Zbl 0097.28602 · doi:10.1007/BF01450934
[15] DOI: 10.1142/S0129167X9500050X · Zbl 0865.14004 · doi:10.1142/S0129167X9500050X
[16] Huybrechts D., J. Algebraic Geom. 4 pp 67–
[17] DOI: 10.1007/978-3-663-11624-0 · doi:10.1007/978-3-663-11624-0
[18] Kleiman S., Compos. Math. 41 pp 39–
[19] DOI: 10.1007/978-3-642-57916-5 · Zbl 0797.14004 · doi:10.1007/978-3-642-57916-5
[20] DOI: 10.1090/ulect/018 · doi:10.1090/ulect/018
[21] DOI: 10.1007/s00222-005-0444-1 · Zbl 1100.14009 · doi:10.1007/s00222-005-0444-1
[22] Newstead P. E., Tata Institute of Fundamental Research Lectures on Mathematics and Physics 51, in: Introduction to Moduli Problems and Orbit Spaces (1978) · Zbl 0411.14003
[23] DOI: 10.1007/978-3-0348-0151-5 · Zbl 1237.14003 · doi:10.1007/978-3-0348-0151-5
[24] Serre J. P., Séminaires Claude Chevalley 3 pp 1–
[25] DOI: 10.1007/BF01471124 · Zbl 0113.36306 · doi:10.1007/BF01471124
[26] Taylor J. L., Graduate Studies in Mathematics 46, in: Several Complex Variables with Connections to Algebraic Geometry and Lie Groups (2000)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.