By Oscar Zariski
Moduli difficulties in algebraic geometry date again to Riemann's recognized count number of the $3g-3$ parameters had to be certain a curve of genus $g$. during this e-book, Zariski reports the moduli house of curves of a similar equisingularity type. After constructing and reviewing the elemental fabric, Zariski devotes one bankruptcy to the topology of the moduli house, together with an specific choice of the infrequent circumstances while the gap is compact. bankruptcy V appears to be like at particular examples the place the size of the primary part may be decided via quite concrete equipment. Zariski's final bankruptcy matters the appliance of deformation thought to the moduli challenge, together with the choice of the size of the everyday part for a selected relations of curves. An appendix by way of Bernard Teissier reconsiders the moduli challenge from the perspective of deformation idea. He provides new proofs of a few of Zariski's effects, in addition to a ordinary building of a compactification of the moduli house.
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