Sums of three squares and Noether-Lefschetz loci

被引：5
|
作者：
Benoist, Olivier [1 ,2 ]
机构：
[1] Univ Strasbourg, Inst Rech Math Avancee, UMR 7501, 7 Rue Rene Descartes, F-67000 Strasbourg, France
[2] CNRS, 7 Rue Rene Descartes, F-67000 Strasbourg, France
来源：
COMPOSITIO MATHEMATICA | 2018年 / 154卷 / 05期
关键词：
sums of squares; Hodge theory; real algebraic geometry; variations of Hodge structures; POLYNOMIALS; COMPONENTS;
D O I：
10.1112/S0010437X18007017
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
We show that the set of real polynomials in two variables that are sums of three squares of rational functions is dense in the set of those that are positive semidefinite. We also prove that the set of real surfaces in P-3 whose function field has level 2 is dense in the set of those that have no real points.
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页码：1048 / 1065
页数：18
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