Models of Curves
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The main aim of these lectures is to present the stable reduction theorem with the point of view of Deligne and Mumford. We introduce the basic material needed to manipulate models of curves, including intersection theory on regular arithmetic surfaces, blow-ups and blow-downs, and the structure of the jacobian of a singular curve. The proof of stable reduction in characteristic 0 is given, while the proof in the general case is explained and important parts are proved. We give applications to the moduli of curves and covers of curves.
KeywordsAlgebraic curve regular model stable reduction
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