This quantity comprises the complaints of an AMS designated consultation held on the 1999 Joint arithmetic conferences in San Antonio. The members have been a global crew of researchers learning singularities from algebraic and analytic viewpoints. The contributed papers comprise unique effects in addition to a few expository and ancient fabric. This quantity is devoted to Oscar Zariski, at the 100th anniversary of his birth.The themes contain the position of valuation thought in algebraic geometry with contemporary purposes to the constitution of morphisms; algorithmic methods to solution of equisingular floor singularities and in the neighborhood toric forms; susceptible subintegral closures of beliefs and Rees valuations; structures of common weakly subintegral extensions of earrings; direct-sum decompositions of finitely generated modules; building and examples of solution graphs of floor singularities; Jacobians of meromorphic curves; research of spectral numbers of curve singularities utilizing Puiseux pairs; Grobner foundation calculations of Hochschild homology for hypersurfaces with remoted singularities; and the speculation of attribute sessions of singular areas - a quick heritage with conjectures and open difficulties.
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