## Current Developments in MathematicsInternational Press, 2007 - Mathematics |

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### Contents

Three Topics in Additive Prime Number Theory | 1 |

Finite Generation of a Canonical Ring | 43 |

Recent Progress in GWInvariants of CalabiYau Threefolds | 77 |

Copyright | |

3 other sections not shown

### Common terms and phrases

additional vanishing algebraic ample line bundle analytic birational boundary bounded Calabi Calabi-Yau canonical divisor canonical ring Chern class Chow-Mumford coefficients compact complex complex manifold complex Monge-Ampere equation condition conjecture constant scalar curvature convergence curvature current curves decomposition defined denote dichotomy dimension discrepancy subspace equivalence classes estimates exists fiber finite flip Floer homology formula function genus geodesic rays Geom geometry Gromov-Witten invariants GW-invariants holomorphic sections hyperplane property hypersurface ideal sheaf imbedding implies inequality Kahler manifold Kahler metrics Kahler-Einstein metric Kahler-Ricci flow Kodaira Lemma Math minimal model moduli space Monge-Ampere equation morphism multiplier ideal sheaves obstruction theory one-parameter subgroups pluricanonical positive integer primes problem projective variety proof Proposition proved Q-divisor Q-factorial restriction Ricci scalar curvature Seiberg-Witten Floer homology sequence singularities smooth solution spectral flow stability stable vanishing order subvariety symplectic test configuration Tian vanishing theorem Zariski zero