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arXiv · 1908.06945

Abundance for uniruled pairs which are not rationally connected

Vladimir Lazić
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Abstract

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.

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Vladimir Lazić. 2023-04-17. Abundance for uniruled pairs which are not rationally connected. https://doi.org/10.4171/lem%2F1065

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