Abundance for uniruled pairs which are not rationally connected

2019/08/19 by Lazić, Vladimir
#14E30 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1908.06945

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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