Class VII surfaces with $b_2=3$ and two foliations are Kato

Nikon Kurnosov; Calum Spicer

paper

Class VII surfaces with $b_{2} = 3$ and two foliations are Kato

arXiv:2608.29047

Abstract

Let $S$ be a minimal compact complex surface of class VII with $b_{2} (S) = 3$ . We prove that if $S$ carries two distinct singular holomorphic foliations, then $S$ contains a global spherical shell. Moreover, it is an Inoue-Hirzebruch surface. The proof is based on Teleman's theorem on the existence of a cycle of rational curves and results of Dloussky and is inspired by work of Brunella.

arXiv comment25 pages

Class VII surfaces with b2​=3 and two foliations are Kato

Abstract

Class VII surfaces with $b_{2} = 3$ and two foliations are Kato