The cone theorem revisited

The cone theorem revisited

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James McKernan, MIT
417 Mathematics Hall, Columbia

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 Kollár. Finally we will describe a recent proof due to Lehmann of Batyrev's conjecture concerning the nef cone of curves.