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a-degree a-large abelian algebraic set analytic assume bounded branch points bundle C*-algebra canonical Cantor normal form Cauchy-Riemann equations choose closed codimension coefficients compact complex component compute conjecture contained converges Corollary defined definition denote diffeomorphism differential equations dimension disk domain eigenvalues element embedding exact sequence exists extends fiber finite foliated follows Frobenius algebra function Godbillon-Vey harmonic map Hence holomorphic holonomy homeomorphism homogeneous homotopy equivalence hypo-elliptic implies induction integral involution isomorphism Jacobi fields Lemma lens spaces Let G linear manifold master code Math matrix minimal surfaces nonsingular normal notation Note obtain open neighborhood open subset orthogonal p-adic polynomial projection proof of Theorem Proposition prove real number recursive Remark result satisfies Section Sh(G Shimura variety simulates singularities smooth solution space submanifold subspace sufficiently suitable for G Suppose tangent Theorem tion trivial vector fields zero