Birational classification of pointless del Pezzo surfaces of degree 8

被引：1
|
作者：
Trepalin, Andrey [1 ,2 ]
机构：
[1] Russian Acad Sci, Steklov Math Inst, 8 Gubkina Str, Moscow 119991, Russia
[2] Natl Res Univ Higher Sch Econ, Lab Algebra Geometry, 6 Usacheva Str, Moscow 119048, Russia
来源：
EUROPEAN JOURNAL OF MATHEMATICS | 2023年 / 9卷 / 01期
基金：
俄罗斯科学基金会;
关键词：
Del Pezzo surfaces; Quadric surfaces; Brauer group; Sarkisov links; RATIONAL SURFACES;
D O I：
10.1007/s40879-023-00591-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let k be a perfect field. Recently Jean-Louis Colliot-Th & eacute;l & egrave;ne showed that two pointless quadric surfaces over k are birationally equivalent if and only if they are isomorphic. We show that this result holds for arbitrary del Pezzo surfaces of degree 8 with the Picard number 1, and describe minimal surfaces birationally equivalent to a given pointless del Pezzo surface of degree 8.
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