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Stable \(G_ 2\) bundles and algebraically completely integrable systems. (English) Zbl 0806.14019
This paper is based on results of N. Hitchin [Duke Math. J. 54, 90- 114 (1987; Zbl 0627.14024) and Proc. Lond. Math. Soc., III. Ser. 55, 59- 126 (1987; Zbl 0634.53045)] extended by Simpson. Hitchin proved that for any simple compact Lie group \(G\) the cotangent bundle of the moduli space of stable principal \(G\)-bundles over a compact Riemann surface is a completely integrable system. He showed that when \(G\) is one of the classical groups then the generic level set of this integrable system can be compactified to a Jacobian or Prym variety. Analogous results are obtained in this paper for the geometry of the level sets when \(G\) is the exceptional Lie group \(G_ 2\).
Reviewer: F.Kirwan (Oxford)

MSC:
14H10 Families, moduli of curves (algebraic)
14K30 Picard schemes, higher Jacobians
17B45 Lie algebras of linear algebraic groups
37-XX Dynamical systems and ergodic theory
14D20 Algebraic moduli problems, moduli of vector bundles
30F30 Differentials on Riemann surfaces
14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials
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