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By Oscar Zariski

Moduli difficulties in algebraic geometry date again to Riemann's recognized count number of the $3g-3$ parameters had to ascertain a curve of genus $g$. during this publication, Zariski reports the moduli house of curves of an identical equisingularity category. After constructing and reviewing the fundamental fabric, Zariski devotes one bankruptcy to the topology of the moduli area, together with an particular selection of the infrequent situations while the distance is compact. bankruptcy V seems at particular examples the place the size of the regular part might be decided via fairly concrete tools. Zariski's final bankruptcy issues the appliance of deformation thought to the moduli challenge, together with the selection of the measurement of the usual part for a selected relatives of curves. An appendix by means of Bernard Teissier reconsiders the moduli challenge from the viewpoint of deformation conception. He supplies new proofs of a few of Zariski's effects, in addition to a usual development of a compactification of the moduli area.

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