## Recent Progress in Arithmetic and Algebraic Geometry: Barrett Lecture Series Conference, April 25-27, 2002, University of Tennessee, Knoxville, TennesseeThis proceedings volume resulted from the John H. Barrett Memorial Lecture Series held at the University of Tennessee (Knoxville). The articles reflect recent developments in algebraic geometry. It is suitable for graduate students and researchers interested in algebra and algebraic geometry. |

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### Contents

1 | |

Completions of valuation rings | 13 |

A new construction of maximal curves | 35 |

Strong nonisotriviality and rigidity | 47 |

Spectral sequences associated to morphisms of locally free sheaves | 57 |

Holomorphic forms on threefolds | 87 |

The problem of resolution of singularities of morphisms in the logarithmic category | 95 |

Jacobians of quotients of ArtinSchreier curves | 145 |

Gluing schemes and a scheme without closed points | 157 |

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abelian varieties affine scheme Alb(X Algebraic Geometry algorithm assume bimeromorphic birational maps blowups with smooth canonical bundle canonical principalization cp1 characteristic zero closed points closed subscheme compact Kähler compute conjecture construction Corollary curve of genus define denote diagram dominates exists fibers fibration fibre finite étale cover hence holomorphic implies induced irreducible components isomorphism isotrivial Jacobian Kodaira dimension Lemma Let f line bundle locally free sheaves logarithmic category logarithmic ramification divisor logarithmic structures maps onto q Math Mathematics min{io monomials morphism f Newton polygon non-isotrivial normal local ring prime ideal Proposition PSL2(Fq quotient field regular local ring regular parameters resolution of singularities ringed spaces Riog Rog fo Rog.f sequence of blowups smooth centers smooth projective Spec standard neighborhood strict transform Subcase Suppose surjective system of regular T1-general type threefold toroidal torus valuation ring zero locus