$R$-EQUIVALENCE ON DEL PEZZO SURFACES OF DEGREE $4$ AND CUBIC SURFACES - Archive ouverte HAL Access content directly
Journal Articles Taiwanese Journal of Mathematics, TJM Year : 2015

$R$-EQUIVALENCE ON DEL PEZZO SURFACES OF DEGREE $4$ AND CUBIC SURFACES

Zhiyu Tian
  • Function : Author

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 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.

Dates and versions

hal-02320308 , version 1 (18-10-2019)

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Cite

Zhiyu Tian. $R$-EQUIVALENCE ON DEL PEZZO SURFACES OF DEGREE $4$ AND CUBIC SURFACES. Taiwanese Journal of Mathematics, TJM, 2015, 19 (6), pp.1603-1612. ⟨10.11650/tjm.19.2015.5351⟩. ⟨hal-02320308⟩

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