Slope Inequalities for the Geography Problem of Spin Symplectic 4-Manifolds

Shintaro Fushida-Hardy; Robert Harris; B. Doug Park

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arXiv · 2608.25889

Slope Inequalities for the Geography Problem of Spin Symplectic 4-Manifolds

Shintaro Fushida-Hardy·Robert Harris·B. Doug Park

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Abstract

We construct infinitely many new pairwise nondiffeomorphic smooth structures on infinitely many closed simply connected spin 4-manifolds with positive signature. Our construction builds on an infinite family of simply connected complex surfaces of general type due to Roulleau and Urz\'{u}a that populate points arbitrarily near the Bogomolov-Miyaoka-Yau line in the complex geography plane. We also discuss how the conjectural symplectic Bogomolov-Miyaoka-Yau inequality implies that our results are close to being optimal.

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Shintaro Fushida-Hardy, Robert Harris, B. Doug Park. 2026-08-26. Slope Inequalities for the Geography Problem of Spin Symplectic 4-Manifolds. https://arxiv.org/abs/2608.25889

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