English

Anticanonical divisor with good asymptotic base loci

Algebraic Geometry 2025-06-17 v2

Abstract

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

Keywords

Cite

@article{arxiv.2411.04628,
  title  = {Anticanonical divisor with good asymptotic base loci},
  author = {Sung Rak Choi and Sungwook Jang and Dae-Won Lee},
  journal= {arXiv preprint arXiv:2411.04628},
  year   = {2025}
}