Anticanonical divisor with good asymptotic base loci

Sung Rak Choi; Sungwook Jang; Dae-Won Lee

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arXiv · 2411.04628

Anticanonical divisor with good asymptotic base loci

Sung Rak Choi·Sungwook Jang·Dae-Won Lee

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Abstract

In this paper, we give a characterization of Fano type varieties in terms of the asymptotic base loci of $-(K_X+\Delta)$. We also show that for a potentially lc pair $(X,\Delta)$, if no plc centers are contained in the augmented base locus $\mathbf{B}_{+}(-(K_X+\Delta))$, then $(X,\Delta)$ has a good $-(K_X+\Delta)$-minimal model. This gives an analogous result of Birkar--Hu on the existence of good minimal models.

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Sung Rak Choi, Sungwook Jang, Dae-Won Lee. 2024-11-07. Anticanonical divisor with good asymptotic base loci. https://arxiv.org/abs/2411.04628

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