Geometry and analysis of spin equations

Details Geometry and analysis of spin equations Geometry and analysis of spin equations

2004-09-22

arxiv.org/abs/math/0409434v2

Mathematics

Differential Geometry

AMSLaTeX; Minor errors corrected, exposition improved

Scientific paper

We introduce W-spin structures on a Riemann surface and give a precise definition to the corresponding W-spin equations for any quasi-homogeneous polynomial W. Then, we construct examples of nonzero solutions of spin equations in the presence of Ramond marked points. The main result of the paper is a compactness theorem for the moduli space of the solutions of W-spin equations when W is a non-degenerate, quasi-homogeneous polynomial whose variables all have weight (or fractional degree) wt(x_i) < 1/2. In particular, the compactness theorem holds for the A,D, and E superpotentials.

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