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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 

 

Nondegenerate multidimensional matrices and instanton bundles


Authors: Laura Costa and Giorgio Ottaviani
Journal: Trans. Amer. Math. Soc. 355 (2003), 49-55
MSC (2000): Primary 14D21, 14J60; Secondary 15A72
Published electronically: September 6, 2002
MathSciNet review: 1927201
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Abstract: In this paper we prove that the moduli space of rank $2n$ symplectic instanton bundles on ${\mathbb{P} ^{2n+1}}$, defined from the well-known monad condition, is affine. This result was not known even in the case $n=1$, where by Atiyah, Drinfeld, Hitchin, and Manin in 1978 the real instanton bundles correspond to self-dual Yang Mills $Sp(1)$-connections over the $4$-dimensional sphere. The result is proved as a consequence of the existence of an invariant of the multidimensional matrices representing the instanton bundles.


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Additional Information

Laura Costa
Affiliation: Departament Algebra i Geometria, Universitat de Barcelona, Gran Via, 585, 08007 Barcelona, Spain
Email: costa@mat.ub.es

Giorgio Ottaviani
Affiliation: Dipartimento di Matematica “U. Dini", Università di Firenze, viale Morgagni 67/A, I 50134 Firenze, Italy
Email: ottavian@math.unifi.it

DOI: http://dx.doi.org/10.1090/S0002-9947-02-03126-4
Received by editor(s): October 23, 2001
Published electronically: September 6, 2002
Additional Notes: The first author was partially supported by DGICYT BFM2001-3584
The second author was partially supported by Italian MURST
Article copyright: © Copyright 2002 American Mathematical Society