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Polarized pairs, log minimal models, and Zariski decompositions

  • Caucher Birkar (a1) and Zhengyu Hu (a2)

Abstract

We continue our study of the relation between log minimal models and various types of Zariski decompositions. Let (X,B) be a projective log canonical pair. We will show that (X,B) has a log minimal model if either KX + B birationally has a Nakayama–Zariski decomposition with nef positive part, or if KX +B is big and birationally has a Fujita–Zariski or Cutkosky–Kawamata–Moriwaki–Zariski decomposition. Along the way we introduce polarized pairs (X,B +P), where (X,B) is a usual projective pair and where P is nef, and we study the birational geometry of such pairs.

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References

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Polarized pairs, log minimal models, and Zariski decompositions

  • Caucher Birkar (a1) and Zhengyu Hu (a2)

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