Abstract
The aim of this course is to provide an introduction to Mori’s Minimal Model Program (MMP) on smooth projective varieties. We review classical results on Weil and Cartier divisors and define ample and nef divisors. We explain how an asymptotic Riemann–Roch theorem gives a general definition for the intersection number of Cartier divisors. We also go through the construction of the moduli space of morphisms from a fixed curve to a fixed smooth variety, define free curves and uniruled varieties, and state Mori’s bend-and-break lemmas. We finish with a proof of Mori’s cone theorem for smooth projective varieties and explain the basic steps of the MMP. Open image in new window
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