Abstract
We provide a description of the moduli space of framed autodual instanton bundles on projective space, focusing on the particular cases of symplectic and orthogonal instantons. Our description will use the generalized ADHM equations which define framed instanton sheaves.
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R. Abuaf and A. Boralevi. Orthogonal bundles and skew-hamiltonian matrices. Canad. J. Math., 67 (2015), 961–989.
M. Atiyah, V. Drinfeld, N. Hitchin, and Yu Manin. Construction of instantons. Phys. Lett., 65A (1978), 185–187.
V. Ancona and G. Ottaviani. Stability of special instanton bundles on P2n+1. Trans. Amer. Math. Soc., 341 (1994), 677–693.
U. Bruzzo, D. Markushevich and A.S. Tikhomirov. Moduli of symplectic instanton vector bundles of higher rank on projective space P3. Cent. Eur. J. Math., 10(4) (2012), 1232–1245.
L. Costa, N. Hoffmann, R.M. Miró-Roig, and A. Schmitt. Rational families of instanton bundles on P2n+1. Algebr.Geom., 2 (2014), 229–260.
L. Costa and G. Ottaviani. Nondegenerate multidimensionalmatrices and instanton bundles. Trans. Amer. Math. Soc., 355 (2002), 49–55.
I. Coanda, A.S. Tikhomirov and G. Trautmann. Irreducibility and smoothness of themoduli space ofmathematical 5-instantons over P3. Int. J. Math., 14(1) (2003), 1–45.
L. Farnik, D. Frapporti and S. Marchesi. On the non-existence of orthogonal instanton bundles on P2n+1. Le Matematiche Catania, 2 (2009), 81–90.
I.B. Frenkel and M. Jardim. Complex ADHM equations and sheaves on P3. J. Algebra, 319 (2008), 2913–2937.
A. Henni, M. Jardim and R.V. Martins. ADHM construction of perverse instanton sheaves. Glasgow Math. J., 57 (2015), 285–321.
M. Jardim. Atiyah-drinfeld-hitchin-manin construction of framed instanton sheaves. C. R. Acad. Sci. Paris, 346(7-8) (2008), 427–430.
M. Jardim and V.M.F. da Silva. Decomposability criterion for linear sheaves. Cent. Eur. J. Math., 10 (2012), 1292–1299.
M. Jardim and M. Verbitsky. Trihyperkahler reduction and instanton bundles on CP3. CompositioMath., 150 (2014), 1836–1868.
M. Mamone Capria and S.M. Salamon. Yang-mills fields on quaternionic spaces. Nonlinearity, 1(4) (1988), 517–530.
C. Okonek and H. Spindler. Mathematical instanton bundles on P2n+1. J. Reine Angew. Math., 364 (1986), 35–50.
C. Okonek, M. Schneider and H. Spindler. Vector bundles on complex projective spaces. Birkhäuser (1980).
G. Ottaviani. Symplectic bundles on the plane, secant varieties and Lüroth quartics revisited. Quad. Math., 21 (2007), 315–352.
H. Spindler and G. Trautmann. Special instanton bundles on P2n+1, their geometry and their moduli.Math. Ann., 286 (1990), 559–592.
A. Tikhomirov. Moduli of mathematical instanton vector bundles with odd c2 on projective space. Izvestiya: Mathematics, 76 (2012), 991–1073.
A. Tikhomirov. Moduli of mathematical instanton vector bundles with odd c2 on projective space. Izvestiya: Mathematics, 77 (2013), 1331–1355.
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Partially supported by the CNPq grant number 302477/2010-1 and the FAPESP grants number 2011/01071-3 and 2014/14743-8.
Supported by the FAPESP post-doctoral grant number 2012/07481-1.
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Jardim, M., Marchesi, S. & Wissdorf, A. Moduli of autodual instanton bundles. Bull Braz Math Soc, New Series 47, 823–843 (2016). https://doi.org/10.1007/s00574-016-0190-6
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DOI: https://doi.org/10.1007/s00574-016-0190-6