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Geometry and analysis of spin equations
Author(s) -
Fan Huijun,
Jarvis Tyler J.,
Ruan Yongbin
Publication year - 2008
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.20246
Subject(s) - mathematics , compact space , moduli space , spin (aerodynamics) , polynomial , riemann surface , homogeneous , homogeneous polynomial , space (punctuation) , compact riemann surface , pure mathematics , mathematical analysis , mathematical physics , combinatorics , physics , matrix polynomial , linguistics , philosophy , thermodynamics
We introduce W ‐spin structures on a Riemann surface Σ 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 = W ( x 1 , …, x t ) is a nondegenerate, quasi‐homogeneous polynomial with fractional degrees (or weights) q i < ½ for all i . In particular, the compactness theorem holds for the superpotentials E 6 , E 7 , E 8 or A n − 1 , D n + 1 for n ≥ 3. © 2008 Wiley Periodicals, Inc.