## Annals of Mathematics |

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### Contents

Introduction | 38 |

Positivity of cone classes | 49 |

Appendix B The theorem of Bloch and Gieseker | 57 |

### Common terms and phrases

algebraic ample vector bundles analytic hypoelliptic assume Banach spaces Bergman metric boundary bounded C*-algebra Chern class class field theory commutative compact complete components cone conic neighborhood conjugacy consider constant construct coordinates Corollary corresponding curvature curve cusps defined denote differential eigenvalues elliptic equation equivalence ergodic exact sequence exists extension fact fibre space finite fixed foliation follows formula function geometric given Hence homomorphism horocycle horocycle flow hypoelliptic implies induced inequality integral intersection invariant isomorphic K3 surfaces kernel lattice Lemma Lie group line bundle linear Math maximal minimal Moreover neighborhood nodes norm obtain operator p-adic analytic polynomial positive pro-p group proof of Theorem Proposition prove punctures quotient representation result satisfies Section singularities smooth solution subgroup subset subspace sufficiently small Suppose surface tangent topology transverse trivial unique unstable manifolds vector bundle vector fields zero