3 problems

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Tom Dieck–Petrie conjecture for homology planes
Let $X$ be a homology plane, meaning a smooth quasi-projective surface with the same integral homology as $\mathbb{C}^2$ , of log-general type, and let $(\bar{X},D)$ be a minimal SN…
Conjectureopenalgebraic-surfaces homology-planes log-general-typearXiv posted 2 days ago
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Tom Dieck--Petrie's optimal-divisor conjecture for $cZ$ -homology planes
Tom Dieck--Petrie Conjecture. The surface $S$ has an optimal divisor on $cmathbb{P}^2$ or on a Hirzebruch surface $cmathbb{F}_m$ .
Conjectureopenalgebraic-surfaces homology-planesarXiv posted 2 days ago
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The linear plane divisor conjecture for smooth Q-homology planes of general type
Linear plane divisor conjecture. Every smooth $cQ$ -homology plane of general type has a linear plane divisor.
Conjecturerefutedaffine-surfaces algebraic-surfaces homology-planesarXiv posted 2 days ago

Tom Dieck–Petrie conjecture for homology planes