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arXiv · 2608.22333

Unirational Fano threefolds

Alex Massarenti
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Abstract

We use the relative Abel--Jacobi construction of Cheltsov--Loginov--Orlov--Prokhorov to study unirational Fano threefolds. Our main result is a $50$-dimensional family of smooth unirational del Pezzo threefolds of degree one. We also construct explicit one-parameter families of terminal unirational sextic double solids and quartic threefolds of Picard rank one. Finally, we reinterpret the Roth--Iskovskikh unirationality construction for smooth double quadric threefolds in terms of a correspondence induced by the relative Abel--Jacobi map.

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Alex Massarenti. 2026-08-23. Unirational Fano threefolds. https://arxiv.org/abs/2608.22333

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