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arXiv · 2607.16753

Non-general type surfaces in P4, an update

Hirotachi Abo·Kristian Ranestad·Frank-Olaf Schreyer
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Abstract

A general algebraic surface cannot be embedded in P4. Proving a conjecture by Hartshorne and Lichtenbaum, Ellingsrud and Peskine showed that there is a degree bound for smooth rational surfaces in P4, and in fact for surfaces not of general type. We give a survey of the classification status and of classical and computer-aided constructions of smooth non-general type surfaces in P4.

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Hirotachi Abo, Kristian Ranestad, Frank-Olaf Schreyer. 2026-07-18. Non-general type surfaces in P4, an update. https://arxiv.org/abs/2607.16753

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