2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/155443We 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.AMSLaTeX; Minor errors corrected, exposition improvedDifferential GeometryAlgebraic GeometryAnalysis of PDEsSymplectic Geometry58J05; 53D45;14H15;32G13text