Models of Curves

  • Matthieu RomagnyEmail author
Conference paper
Part of the Progress in Mathematics book series (PM, volume 304)


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.


Algebraic curve regular model stable reduction 


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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Institut de MathématiquesUniversité Pierre et Marie CurieParis Cedex 05France

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