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| Format: | Preprint |
| Published: |
2019
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/1908.06945 |
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Table of Contents:
- One of the central aims of the Minimal Model Program is to show that a projective log canonical pair $(X,Δ)$ with $K_X+Δ$ pseudoeffective has a good model, i.e.\ a minimal model $(Y,Δ_Y)$ such that $K_Y+Δ_Y$ is semiample. The goal of this paper is to show that this holds if $X$ is uniruled but not rationally connected, assuming the Minimal Model Program in dimension $\dim X-1$. Moreover, if $X$ is rationally connected, then we show that the existence of a good minimal model for $(X,Δ)$ follows from a nonexistence conjecture for a very specific class of rationally connected pairs of Calabi--Yau type.