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| Format: | Preprint |
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2019
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| Online Access: | https://arxiv.org/abs/1908.06945 |
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| _version_ | 1866911112506638336 |
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| author | Lazić, Vladimir |
| author_facet | Lazić, Vladimir |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1908_06945 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | Abundance for uniruled pairs which are not rationally connected Lazić, Vladimir Algebraic Geometry 14E30 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. |
| title | Abundance for uniruled pairs which are not rationally connected |
| topic | Algebraic Geometry 14E30 |
| url | https://arxiv.org/abs/1908.06945 |