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arXiv · 1307.1801

R-equivalence on del Pezzo surfaces of degree 4 and cubic surfaces

Zhiyu Tian
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Abstract

We prove that there is a unique $R$-equivalence class on every del Pezzo surface of degree $4$ defined over the Laurent field $K=k((t))$ in one variable over an algebraically closed field $k$ of characteristic not equal to $2$ or $5$. We also prove that given a smooth cubic surface defined over $\mathbb{C}((t))$, if the induced morphism to the GIT compactification of smooth cubic surfaces lies in the stable locus (possibly after a base change), then there is a unique $R$-equivalence class.

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Zhiyu Tian. 2014-04-02. R-equivalence on del Pezzo surfaces of degree 4 and cubic surfaces. https://arxiv.org/abs/1307.1801

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