Termination of (many) 4-dimensional log flips

• Autores: Valery Alexeev, Christopher D. Hacon, Yujiro Kawamata
• Localización: Inventiones mathematicae, ISSN 0020-9910, Vol. 168, Nº. 2, 2007, págs. 433-448
• Idioma: inglés
• DOI: 10.1007/s00222-007-0038-1
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• Resumen

  • 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.