English

$K$-polystability of smooth Fano $\text{SL}_2$-threefolds

Algebraic Geometry 2022-01-12 v1

Abstract

We prove the KK-polystability of all smooth complex Fano threefolds admitting an effective action of SL2\text{SL}_2 but not of a 2-torus or 3-torus. In particular, the existence of K\"{a}hler-Einstein metrics on varieties in the families (1.10), (1.15), (1.16), (1.17), (2.21), (2.27), (2.32), (3.13), (3.17), (3.25) and (4.6) of the Mori-Mukai classification of smooth Fano threefolds is proved.

Keywords

Cite

@article{arxiv.2201.04097,
  title  = {$K$-polystability of smooth Fano $\text{SL}_2$-threefolds},
  author = {Jack Rogers},
  journal= {arXiv preprint arXiv:2201.04097},
  year   = {2022}
}

Comments

59 pages, 19 figures