## Current Topics in Complex Algebraic GeometryClemens Herbert, Herbert Clemens, Janos Kollár, Janos Kollar The 1992/93 academic year at the Mathematical Sciences Research Institute was devoted to complex algebraic geometry. This volume collects survey articles that arose from this event, which took place at a time when algebraic geometry was undergoing a major change. The editors of the volume, Herbert Clemens and János Kollár, chaired the organizing committee. This book gives a good idea of the intellectual content of the special year and of the workshops. Its articles represent very well the change of direction and branching out witnessed by algebraic geometry in the last few years. |

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### Contents

Recent Results in Higher Dimensional Birational Geometry | 35 |

An Update | 57 |

Adjoint Linear Systems | 87 |

Vector bundles and BrillNoether theory | 145 |

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### Common terms and phrases

Ag(L algebraic geometry algebraic varieties base point Beauville biextension birational cameral cover canonical bundle cohomology component computation conjecture construction corresponding curve of genus cycles decomposition defined Denote dimension equivalence exact sequence fiber finite index flips follows fundamental group genus g Higgs bundles Hitchin homology homomorphism induces integrable intermediate Jacobian irreducible isomorphism lattice Lazarsfeld Lemma line bundle locus log terminal mapping class group Math Mg(L mixed Hodge structure moduli space monodromy monodromy representation Mori fibration morphism MSRI nef and big nilpotent normal functions open subset parametrized Pic(S Picard polarized abelian variety polynomial preprint principally polarized abelian projective variety proof Proposition proved Prym Q-factorial quotient rational result semistable smooth projective variety spectral covers subgroup subvariety surjective SUx(r symplectic theorem theory theta divisor theta functions threefolds topology Torelli group torsion torsion-free trivial vanishing variation of Hodge variations of mixed vector bundles Verlinde formula weight Zariski