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Lattices and Rational Points [PDF]

Mathematics, 2017
In this article, we show how to use the first and second Minkowski Theorems and some Diophantine geometry to bound explicitly the height of the points of rank N - 1 on transverse curves in E N , where E is an elliptic curve without Complex
Evelina Viada
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Counting rational points of a Grassmannian

Monatshefte Fur Mathematik, 2022
We prove an estimate on the number of rational points on the Grassmannian variety of bounded twisted height, refining the classical results of Schmidt ([12]) and Thunder ([20]) over the rational field: most importantly, our formula counts all points. Among the consequences are a couple of new implications on the classical subject of counting rational ...
Seungki Kim
exaly   +4 more sources

Rational Cohomology Fixed Points [PDF]

Advances in Group Theory and Applications, 2023
For n ∈ N, we introduce the notion of n-rational cohomology fixed points and we prove, under a certain assumption, that if X is a rational space, then X admits an (n - 1)-rational cohomology fixed point, where n = max{i : kn ≠ 0}.
Mahmoud Benkhalifa
doaj   +1 more source

Quartic surfaces, their bitangents and rational points [PDF]

Épijournal de Géométrie Algébrique, 2023
Let X be a smooth quartic surface not containing lines, defined over a number field K. We prove that there are only finitely many bitangents to X which are defined over K.
Pietro Corvaja, Francesco Zucconi
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On homogeneous spaces with finite anti-solvable stabilizers

Comptes Rendus. Mathématique, 2022
We say that a group is anti-solvable if all of its composition factors are non-abelian. We consider a particular family of anti-solvable finite groups containing the simple alternating groups for $n\ne 6$ and all 26 sporadic simple groups. We prove that,
Lucchini Arteche, Giancarlo
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Which rational double points occur on del Pezzo surfaces? [PDF]

Épijournal de Géométrie Algébrique, 2021
We determine all configurations of rational double points that occur on RDP del Pezzo surfaces of arbitrary degree and Picard rank over an algebraically closed field $k$ of arbitrary characteristic ${\rm char}(k)=p \geq 0$, generalizing classical work of
Claudia Stadlmayr
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Parametrization of Algebraic Points of Low Degrees on the Schaeffer Curve

Journal of Mathematical Sciences and Modelling, 2021
In this paper, we give a parametrization of algebraic points of degree at most $4$ over $\mathbb{Q}$ on the schaeffer curve $\mathcal{C}$ of affine equation : $ y^{2}=x^{5}+1 $. The result extends our previous result which describes in [5] ( Afr.
Moussa Fall
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Rational points on quartics [PDF]

Duke Mathematical Journal, 2000
32 pages ...
Harris, Joe, Tschinkel, Yuri
openaire   +4 more sources

New sequences of non-free rational points

Comptes Rendus. Mathématique, 2021
We exhibit some new infinite families of rational values of $\tau $, some of them squares of rationals, for which the group or even the semigroup generated by the matrices $({{\textstyle \begin{matrix} 1 & 1\\ 0 & 1 \end{matrix}}})$ and  $({{\textstyle ...
Smilga, Ilia
doaj   +1 more source

Quartic and Quintic Hypersurfaces with Dense Rational Points

Forum of Mathematics, Sigma, 2023
Let $X_4\subset \mathbb {P}^{n+1}$ be a quartic hypersurface of dimension $n\geq 4$ over an infinite field k. We show that if either $X_4$ contains a linear subspace $\Lambda $ of dimension $h\geq \max \{2,\dim (\Lambda ...
Alex Massarenti
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