Sums of three squares and Noether–Lefschetz loci

Author:

Benoist Olivier

Abstract

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 $\mathbb{P}^{3}$ whose function field has level 2 is dense in the set of those that have no real points.

Publisher

Wiley

Subject

Algebra and Number Theory

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2. General components of the Noether-Lefschetz locus and their density in the space of all surfaces

3. Divisors on real algebraic varieties without real points

Cited by 3 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. OUP accepted manuscript;The Quarterly Journal Of Mathematics;2021

2. Existence and Density of General Components of the Noether–Lefschetz Locus on Normal Threefolds;International Mathematics Research Notices;2020-02-05

3. The period-index problem for real surfaces;Publications mathématiques de l'IHÉS;2019-05-28

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