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Geometry and analysis of spin equations

Huijun Fan·Tyler J. Jarvis·Yongbin Ruan
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Abstract

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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Huijun Fan, Tyler J. Jarvis, Yongbin Ruan. 2008-02-23. Geometry and analysis of spin equations. https://arxiv.org/abs/math/0409434

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