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arXiv · 2512.19660

Birational geometry of del Pezzo surfaces of degree 4

Constantin Shramov·Andrey Trepalin
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Abstract

It is known that any Mori fiber space birational to a minimal smooth del Pezzo surface $S$ of degree $4$ is either a del Pezzo surface of degree $4$ itself, or a smooth cubic surface with a structure of a relatively minimal conic bundle. We show that any del Pezzo surface of degree $4$ birational to $S$ is actually isomorphic to $S$. Also, we sketch an equivariant version of this fact. On the way, we review the biregular classification of del Pezzo surfaces of degree $4$ obtained by A. N. Skorobogatov.

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Constantin Shramov, Andrey Trepalin. 2025-12-22. Birational geometry of del Pezzo surfaces of degree 4. https://arxiv.org/abs/2512.19660

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