Results 1 to 10 of about 134,696 (267)
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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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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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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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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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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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
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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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Rational points on a certain genus 2 curve
Comptes Rendus. Mathématique, 2023 We give a correct proof to the fact that all rational points on the curve \[ y^2=(x^2+1)(x^2+3)(x^2+7) \] are $\pm \infty $ and $(\pm 1,\,\pm 8)$. This corrects previous works of Cohen [3] and Duquesne [4, 5].
Nguyen, Xuan Tho
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On rational points in CFT moduli spaces
Journal of High Energy Physics, 2021 Motivated by the search for rational points in moduli spaces of two-dimensional conformal field theories, we investigate how points with enhanced symmetry algebras are distributed there.
Nathan Benjamin +3 more
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Heights on stacks and a generalized Batyrev–Manin–Malle conjecture
Forum of Mathematics, Sigma, 2023 We define a notion of height for rational points with respect to a vector bundle on a proper algebraic stack with finite diagonal over a global field, which generalizes the usual notion for rational points on projective varieties.
Jordan S. Ellenberg +2 more
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