Termination of (many) 4-dimensional log flips |
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Authors: | Valery Alexeev Christopher Hacon Yujiro Kawamata |
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Institution: | (1) Department of Mathematics, University of Georgia, Athens, GA 30602, USA;(2) Department of Mathematics, University of Utah, Salt Lake City, UT 84112-0090, USA;(3) Department of Mathematical Sciences, University of Tokyo, Komaba, Meguro Tokyo, 153-8914, Japan |
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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
X
+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
X
+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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Keywords: | |
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