Higher Dimensional Varieties and their Moduli Spaces

Guanajuato, Mexico
  • Paolo CasciniEmail author
Part of the Lecture Notes of the Unione Matematica Italiana book series (UMILN, volume 21)


To explain some of the main ideas of the Minimal Model Program and some of the tools used, we use some basic facts from graph theory. In particular, we describe a directed graph associated to the category of projective varieties. For this reason, we recall some of the basic definitions in graph theory.



These are the notes for the CIMPA-CIMAT-ICTP School “Moduli of Curves” in Guanajuato, México, 22 February–4 March 2016. I would like to thank the organisers and all the participants for the invitation and for giving me the opportunity to present this material at the school. I would also like to thank the referee for reading a preliminary version of these notes and providing many useful comments.


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Copyright information

© The Author(s) 2017

Authors and Affiliations

  1. 1.Imperial College LondonLondonUK

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