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Termination of (many) 4-dimensional log flips

Valery Alexeev·Christopher Hacon·Yujiro Kawamata
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Abstract

We prove that any sequence of 4-dimensional log flips that begins with a klt pair (X,D) such that -(K+D) is numerically equivalent to an effective divisor, terminates. This implies termination of flips that begin with a log Fano pair and termination of flips in a relative birational setting. We also prove termination of directed flips with big K+D. As a consequence, we prove existence of minimal models of 4-dimensional dlt pairs of general type, existence of 5-dimensional log flips, and rationality of Kodaira energy in dimension 4.

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Valery Alexeev, Christopher Hacon, Yujiro Kawamata. 2006-05-04. Termination of (many) 4-dimensional log flips. https://doi.org/10.1007/s00222-007-0038-1

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