Towards the termination of flips.

Towards the termination of flips.

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Christopher Hacon, The University of Utah
Fine Hall 322

The minimal model program (MMP) predicts that if X is a smooth complex projective variety which is not uniruled, then there is a finite sequence of "elementary" birational maps X=X_0-->X_1-->X_2-->...-->X_n known as divisorial contractions and flips whose output \bar X=X_n  is a minimal model so that K_{\bar X} is a nef Q-divisor i.e it intersects all curves C\subset \bar X

non-negatively: K_{\bar X}\cdot C\geq 0. The existence of these birational maps has been established, but in order to complete the MMP, it is necessary to show that flips terminate i.e.  there are no infinite sequences of flips. In this talk we will discuss recent results towards the termination of flips.