The cone theorem revisited -- James McKernan, February 29, 2008

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We describe a new proof of the cone theorem which follows Mori's original
approach more closely.  At the same time, we will describe a new proof of an
extension of the cone theorem, which is originally due to Ambro and which in
turn is an extension of the cone theorem due to Koll&aacute;r.  Finally we will
describe a recent proof due to Lehmann of Batyrev's conjecture concerning
the nef cone of curves.