Taiwanese Journal of Mathematics

$R$-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.

Article information

Source
Taiwanese J. Math., Volume 19, Number 6 (2015), 1603-1612.

Dates
First available in Project Euclid: 4 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1499133729

Digital Object Identifier
doi:10.11650/tjm.19.2015.5351

Mathematical Reviews number (MathSciNet)
MR3434267

Zentralblatt MATH identifier
1357.14050

Subjects
Primary: 14D10: Arithmetic ground fields (finite, local, global) 14G20: Local ground fields

Keywords
del Pezzo surface $R$-equivalence Laurent field

Citation

Tian, Zhiyu. $R$-EQUIVALENCE ON DEL PEZZO SURFACES OF DEGREE $4$ AND CUBIC SURFACES. Taiwanese J. Math. 19 (2015), no. 6, 1603--1612. doi:10.11650/tjm.19.2015.5351. https://projecteuclid.org/euclid.twjm/1499133729


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