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

We prove that there is a uniqueR-equivalence class on every del Pezzo surface of degree 4 defined over the Laurent fieldK=k((t)) in one variable over an algebraically closed fieldkof characteristic not equal to 2 or 5. We also prove that given a smooth cubic surface defined over ℂ ((t)), if the indu...

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Bibliographic Details
Published inTaiwanese journal of mathematics Vol. 19; no. 6; pp. 1603 - 1612
Main Author Tian, Zhiyu
Format Journal Article
LanguageEnglish
Published Mathematical Society of the Republic of China 01.12.2015
Mathematical Society of the Republic of China (Taiwan)
Subjects
Algebra
Compactification
Conic sections
Gastrointestinal tract
Hypersurfaces
Mathematical surfaces
Mathematical theorems
Mathematics
Morphisms
Series convergence
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Summary:We prove that there is a uniqueR-equivalence class on every del Pezzo surface of degree 4 defined over the Laurent fieldK=k((t)) in one variable over an algebraically closed fieldkof 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 uniqueR-equivalence class. 2010Mathematics Subject Classification: 14D10, 14G20. Key words and phrases: del Pezzo surface,R-equivalence, Laurent field.
ISSN:1027-5487
2224-6851
DOI:10.11650/tjm.19.2015.5351