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Non-trivial harmonic spinors on generic algebraic surfaces. (English) Zbl 0878.58057
The author shows that the space of harmonic spinors on a simply connected algebraic surface is larger than what is predicted by the index theorem. Moreover, its dimension is larger than the absolute value of the index by an arbitrary large number.

58J60 Relations of PDEs with special manifold structures (Riemannian, Finsler, etc.)
58A50 Supermanifolds and graded manifolds
58J20 Index theory and related fixed-point theorems on manifolds
14J99 Surfaces and higher-dimensional varieties
Full Text: DOI arXiv
[1] F. Catanese, On the moduli spaces of surfaces of general type, J. Differential Geom. 19 (1984), no. 2, 483 – 515. · Zbl 0549.14012
[2] F. Catanese, Automorphisms of rational double points and moduli spaces of surfaces of general type, Compositio Math. 61 (1987), no. 1, 81 – 102. · Zbl 0615.14021
[3] Nigel Hitchin, Harmonic spinors, Advances in Math. 14 (1974), 1 – 55. · Zbl 0284.58016 · doi:10.1016/0001-8708(74)90021-8 · doi.org
[4] D. Kotschick, Nontrivial harmonic spinors on certain algebraic surfaces, Einstein metrics and Yang-Mills connections (Sanda, 1990) Lecture Notes in Pure and Appl. Math., vol. 145, Dekker, New York, 1993, pp. 85 – 88. · Zbl 0790.53051
[5] Marco Manetti, On some components of moduli space of surfaces of general type, Compositio Math. 92 (1994), no. 3, 285 – 297. · Zbl 0849.14016
[6] Boris Moishezon and Mina Teicher, Simply-connected algebraic surfaces of positive index, Invent. Math. 89 (1987), no. 3, 601 – 643. · Zbl 0627.14019 · doi:10.1007/BF01388987 · doi.org
[7] E. Witten, Monopoles and \(4\)–manifolds, Math. Research Letters 1 (1994), 769–796. CMP 95:05
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