Smooth $\mathbb{Q}$-homology planes satisfying the Negativity Conjecture

Tomasz Pełka

A complex algebraic surface $S$ is a $\mathbb{Q}$-homology plane if $H_i(S,\mathbb{Q})=0$ for $i>0$. The Negativity Conjecture of Palka asserts that $κ(K_{X}+\tfrac{1}{2}D)=-\inf…