Non–trivial harmonic spinors on generic algebraic surfaces

Kotschick, D.

doi:10.1090/S0002-9939-96-03772-0

Non–trivial harmonic spinors on generic algebraic surfaces
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Proc. Amer. Math. Soc. 124 (1996), 2315-2318 Request permission

Abstract:

We show that there are simply connected spin algebraic surfaces for which all complex structures in certain components of the moduli space admit more harmonic spinors than predicted by the index theorem (or Riemann–Roch). The dimension of the space of harmonic spinors can exceed the absolute value of the index by an arbitrarily large number.

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