The Global Spherical Shell conjecture for minimal class VII surfaces with positive second Betti number

Lineage and corrections

This event attributed to Unreleased internal OpenAI model

The Global Spherical Shell conjecture for minimal class VII surfaces with positive second Betti number evidence for this event

VibeMathed record: The Global Spherical Shell conjecture for minimal class VII surfaces with positive second Betti number evidence for this event

The Global Spherical Shell conjecture for minimal class VII surfaces with positive second Betti number parent of this event

Theorem 1.1: every minimal class VII surface with $b_2>0$ contains a global spherical shell. Corollaries: by Kato, each such surface deforms to blown-up primary Hopf surfaces, has $\pi_1\cong\mathbb Z$ and is diffeomorphic to $(S^1\times S^3)\#b_2\overline{\mathbb{CP}}^2$; and aspherical compact complex surfaces satisfy $\chi\ge\tfrac95|\sigma|$. The proof builds divisors on the infinite cyclic cover and shows all their components are compact rational curves, then applies Dloussky-Oeljeklaus-Toma. It does not give a complete biholomorphic classification of the resulting Kato surfaces beyond what Kato's theory provides. parent of this event