## Advanced Studies in Pure Mathematics 50: Algebraic Geometry in East Asia-Hanoi 2005This volume is the outcome of the conference “Algebraic Geometry in East Asia. II” which was held at the Conference Hall (Hanoi, Vietnam) during October 10 – October 14, 2005. It collects two survey articles and eight research articles contributed by the invited lecturers. Topics touched upon in this volume include: Zariski pairs, rational homogeneous manifolds, Kummer surfaces, singularity theory, Cremona groups, algebraic curves, dual varieties, Castelnuovo–Weil lattices and so on. The reader can not only find the current status of a variety of research topics but also enjoy the art of the subjects by leading algebraic geometers.Published by Mathematical Society of Japan and distributed by World Scientific Publishing Co. for all markets except North America |

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### Contents

Introduction | 10 |

Alexander invariants | 36 |

Nonabelian branched coverings and Zariski pairs | 59 |

Copyright | |

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### Common terms and phrases

abelian affine Alexander polynomials associated automorphism base point free basis birational braid group braid monodromy factorization called Cartan characteristic varieties coefficients combinatorial conic consider corresponding Cx(v defined Definition degree denote diagram divisor double covering double points dual duality elliptic fibration elliptic parameter elliptic root system elliptic singularities equation equivalent Example exists exponents fiber finite formal parameter system function fundamental group G-orbit geometry given Hence homomorphism hyperplane hypersurface induces integer intersection invariant irreducible components isomorphic K3 surfaces lattice Lemma Math maximal meridians Milnor minimal rational tangents module morphism normal Note obtain pencil primitive form projective Proof Proposition regular system Remark resp sextics simple Lie algebra simple singularity singular point smooth subscheme subspace surface surjective system of weights Theorem theory topology transformation triangulated category vanishing cycles variety of minimal Weierstrass equation weight system Weyl group Xw,o Zariski pairs