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MODULI SPACES OF FRAMED PERVERSE INSTANTONS ON ℙ3

Published online by Cambridge University Press:  25 August 2010

MARCIN HAUZER  and
ADRIAN LANGER
MARCIN HAUZER
Affiliation:
Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097 Warszawa, Poland
ADRIAN LANGER
Affiliation:
Institute of Mathematics, Warsaw University, ul. Banacha 2, 02-097, Warszawa, Poland and Institute of Mathematics, Polish Academy of Sciences, ul. Śniadeckich 8, 00-956 Warszawa, Poland e-mail: alan@mimuw.edu.pl
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Abstract

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We study moduli spaces of framed perverse instantons on ℙ3. As an open subset, it contains the (set-theoretical) moduli space of framed instantons studied by I. Frenkel and M. Jardim in [9]. We also construct a few counter-examples to earlier conjectures and results concerning these moduli spaces.

Keywords

Primary: 14D21Secondary: 14F0514J60
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 53 , Issue 1 , January 2011 , pp. 51 - 96
Copyright
Copyright © Glasgow Mathematical Journal Trust 2010

References

REFERENCES

1.Atiyah, M. F., Geometry of Yang–Mills fields (Scuola Normale Superiore Pisa, Pisa, 1979).Google Scholar
2.Beauville, A., Vector bundles on the cubic threefold, in Symposium in honor of C. H. Clemens, Contemporary Mathematics, vol. 312 (Bertram, A., Carlson, J. A. and Kley, H., Editors) (American Mathematical Society, Providence, RI, 2002), 71–86.Google Scholar
3.Ben-Zvi, D. and Nevins, T., Perverse bundles and Calogero–Moser spaces, Compos. Math. 144 (2008), 1403–1428.Google Scholar
4.Braverman, A., Finkelberg, M. and Gaitsgory, D., Uhlenbeck spaces via affine Lie algebras, Prog. Math. 244, 2006, 17–135.Google Scholar
5.Coandă, I., The Chern classes of the stable rank 3 vector bundles on ℙ3, Math. Ann. 273 (1985), 65–79.Google Scholar
6.Coandă, I., Tikhomirov, A. and Trautmann, G., Irreducibility and smoothness of the moduli space of mathematical 5-instantons over ℙ3, Int. J. Math. 14 (2003), 1–45.Google Scholar
7.Diaconescu, D. E., Moduli of ADHM sheaves and local Donaldson–Thomas theory, preprint, arXiv:0801.0820.Google Scholar
8.Donaldson, S. K., Instantons and geometric invariant theory, Commun. Math. Phys. 93 (1984), 453–460.CrossRefGoogle Scholar
9.Frenkel, I. B. and Jardim, M., Complex ADHM data and sheaves on ℙ3, J. Algebra 319 (2008), 2913–2937.Google Scholar
10.Gerstenhaber, M., On dominance and varieties of commuting matrices, Ann. Math. 73 (1961), 324–348.Google Scholar
11.Grothendieck, A., Revêtements étales et groupe fondamental (SGA 1), in Séminaire de géométrie algébrique du Bois Marie 1960–1961, Documents Mathématiques, vol. 3 (Société Mathématique de France, Paris, 2003), xviii + 327 pp.Google Scholar
12.Holbrook, J. and Omladič, M., Approximating commuting operators, Linear Algebra Appl. 327 (2001), 131–149.CrossRefGoogle Scholar
13.Happel, D., Reiten, I. and Smalø, S. O., Tilting in abelian categories and quasitilted algebras, Mem. Amer. Math. Soc. 120 (1996), viii + 88 pp.Google Scholar
14.Huybrechts, D. and Lehn, M., Framed modules and their moduli, Int. J. Math. 6 (1995), 297–324.Google Scholar
15.Huybrechts, D. and Lehn, M., The geometry of moduli spaces of sheaves, Asp. Math. 31 (1997), xiv + 269 pp.Google Scholar
16.Ishimura, S., A descent problem of vector bundles and its applications, J. Math. Kyoto Univ. 23 (1983), 73–83.Google Scholar
17.Jardim, M., Moduli spaces of framed instanton sheaves on projective spaces, arXiv:0801.2550v2.Google Scholar
18.Jardim, M., Atiyah–Drinfeld–Hitchin–Manin construction of framed instanton sheaves, C. R. Math. Acad. Sci. Paris 346 (2008), 427–430.Google Scholar
19.Kaledin, D., Lehn, M. and Sorger, Ch., Singular symplectic moduli spaces, Invent. Math. 164 (2006), 591–614.Google Scholar
20.Katsylo, P. and Ottaviani, G., Regularity of the moduli space of instanton bundles MIP3(5), Transform. Groups 8 (2003), 147–158.CrossRefGoogle Scholar
21.King, A., Moduli of representations of finite-dimensional algebras, Q. J. Math. Oxford Ser. (2) 45 (1994), 515–530.CrossRefGoogle Scholar
22.Kraft, H. and Procesi, C., Classical invariant theory. A primer, preprint (1996).Google Scholar
23.Langer, A., Moduli spaces of sheaves in mixed characteristic, Duke Math. J. 124 (2004), 571–586.Google Scholar
24.Langer, A., Instanton bundles, Arbeitstagung 2007, MPI preprint 07-75.Google Scholar
25.Le Potier, J., Sur l'espace de modules des fibrés de Yang et Mills, in Mathematics and physics (Paris, 1979/1982), Progress in Mathematics, vol. 37 (de Monvel, L. B., Douady, A. and Verdier, J.-L., Editors) (Boston, MA, 1983), 65–137.Google Scholar
26.Morrison, K., The scheme of finite-dimensional representations of an algebra, Pacific J. Math. 91 (1980), 199–218.Google Scholar
27.Motzkin, T. S. and Taussky, O., Pairs of matrices with property L. II, Trans. Amer. Math. Soc. 80 (1955), 387–401.Google Scholar
28.Nakajima, H., Lectures on Hilbert schemes of points on surfaces, University Lecture Series, vol. 18 (American Mathematical Society, Providence, RI, 1999), xii + 132 pp.Google Scholar
29.O'Grady, K., Desingularized moduli spaces of sheaves on a K3, J. Reine Angew. Math. 512 (1999), 49–117.Google Scholar
30.Okonek, C., Schneider, M. and Spindler, H., Vector bundles on complex projective spaces, Progress in Mathematics 3 (Birkhaüser, Boston, Mass., 1980).Google Scholar
31.Procesi, C., Finite dimensional representations of algebras, Israel J. Math. 19 (1974), 169–182.Google Scholar
32.Rao, A. P., Mathematical instantons in characteristic two, Compositio Math. 119 (1999), 169–184.Google Scholar
33.Sawon, J., Twisted Fourier-Mukai transforms for holomorphic symplectic four-folds, Adv. Math. 218 (2008), 828–864.Google Scholar
34.Schmitt, A. H. W., Geometric invariant theory and decorated principal bundles, in Zurich Lectures in Advanced Mathematics (European Mathematical Society (EMS), Zürich, 2008).Google Scholar
35.Sorger, Ch., Lectures on moduli of principal G-bundles over algebraic curves, School on Algebraic Geometry (Trieste, 1999), 1–57, ICTP Lecture Notes, vol. 1 (Göttsche, L., Editor) (Abdus Salam International Centre for Theoretical Physics, Trieste, Italy, 2000).Google Scholar
36.Valli, G., Bi-invariant Grassmannians and Atiyah-Jones theorems, Topol. 39 (2000), 1–31.Google Scholar
37.Varagnolo, M. and Vasserot, E., On the K-theory of the cyclic quiver variety, Int. Math. Res. Notices 18 (1999), 1005–1028.Google Scholar