Littérature scientifique sur le sujet « Transformation birationnelle »
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Articles de revues sur le sujet "Transformation birationnelle"
Déserti, Julie. « Experiments on some birational quadratic transformations ». Nonlinearity 21, no 6 (15 mai 2008) : 1367–83. http://dx.doi.org/10.1088/0951-7715/21/6/013.
Texte intégralCantat, Serge. « Sur les groupes de transformations birationnelles des surfaces ». Annals of Mathematics 174, no 1 (1 juillet 2011) : 299–340. http://dx.doi.org/10.4007/annals.2011.174.1.8.
Texte intégralPan, Ivan, Felice Ronga et Thierry Vust. « Transformations birationnelles quadratiques de l'espace projectif complexe à trois dimensions ». Annales de l’institut Fourier 51, no 5 (2001) : 1153–87. http://dx.doi.org/10.5802/aif.1850.
Texte intégralDéserti, Julie. « Quelques propriétés des transformations birationnelles du plan projectif complexe, une histoire pour S. » Séminaire de théorie spectrale et géométrie 27 (2009) : 45–100. http://dx.doi.org/10.5802/tsg.270.
Texte intégralThèses sur le sujet "Transformation birationnelle"
González-Mazón, Pablo. « Méthodes effectives pour les transformations birationnelles multilinéaires et contributions à l'analyse polynomiale de données ». Electronic Thesis or Diss., Université Côte d'Azur, 2023. http://www.theses.fr/2023COAZ4138.
Texte intégralThis thesis explores two distinct subjects at the intersection of commutative algebra, algebraic geometry, multilinear algebra, and computer-aided geometric design:1. The study and effective construction of multilinear birational maps2. The extraction of information from measures and data using polynomialsThe primary and most extensive part of this work is devoted to multilinear birational maps.A multilinear birational map is a rational map phi: (mathbb{P}^1)^n dashrightarrow{} mathbb{P}^n, defined by multilinear polynomials, which admits an inverse rational map. Birational transformations between projective spaces have been a central theme in algebraic geometry, tracing back to the seminal works of Cremona, which has witnessed significant advancement in the last decades. Additionally, there has been a recent surge of interest in tensor-product birational maps, driven by the study of multiprojective spaces in commutative algebra and their practical application in computer-aided geometric design.In the first part, we address algebraic and geometric aspects of multilinear birational maps.We primarily focus on trilinear birational maps phi: (mathbb{P}^1)^3 dashrightarrow{} mathbb{P}^3, that we classify according to the algebraic structure of their space, base loci, and the minimal graded free resolutions of the ideal generated by the defining polynomials. Furthermore, we develop the first methods for constructing and manipulating nonlinear birational maps in 3D with sufficient flexibility for geometric modeling and design.Interestingly, we discover a characterization of birationality based on tensor rank, which yields effective constructions and opens the door to the application of tools from tensors to birationality. We also extend our results to multilinear birational maps in arbitrary dimension, in the case that there is a multilinear inverse.In the second part, our focus shifts to the application of polynomials in analyzing data and measures.We tackle two distinct problems. Firstly, we derive bounds for the size of (1-epsilon)-nets for superlevel sets of real polynomials. Our results allow us to extend the classical centerpoint theorem to polynomial inequalities of higher degree. Secondly, we address the classification of real cylinders through five-point configurations where four points are cocyclic, i.e. they lie on a circumference. This is an instance of the more general problems of real root classification of systems of real polynomials and the extraction of algebraic primitives from raw data
Durighetto, Sara. « Géométrie birationnelle : classique et dérivée ». Thesis, Toulouse 3, 2019. http://www.theses.fr/2019TOU30031.
Texte intégralIn the field of algebraic geometry, the study of birational transformations and their properties plays a primary role. In this, there are two different approach: the classical one due to the Italian school who focuses on the Cremona group and a modern one which utilizes instruments like derived categories and semiorthogonal decompositions. About the Cremona group, that is the group of birational self- morphisms of Pn, we do not know much in general and we focus on the complex case. We know a set of generators only in dimension n = 2. Moreover, we do not have a classification of curves and linear systems in P2 up to Cremona transformations. Among the known results there are: irreducible curves and curves with two irreducible components. In this thesis we approach tha case of a configuration of lines in the projective plane. The last theorem lists the known contractible configurations. From a categorical point of view, the semiorthogonal decompositions of the derived category of a variety provide some useful invariants in the study of the variety. Following the work of Clemens-Griffiths about the complex cubic threefold, we want to characterize the obstructions to the rationality of a variety X of dimension n. The idea is to collect the component of a semiorthogonal decomposition which are not equivalent to the derived category of a variety of dimension at least n - 1. In this way we defined the so called Griffiths-Kuznetsov component of X. In this thesis we study the case of surfaces on an arbitrary field, we define that component and show that it is a birational invariant. It appears clearly that the Griffiths-Kuznetsov component vanishes only if the surface is rational
Lo, Bianco Federico. « Dynamique des transformations birationnelles des variétés hyperkähleriennes : feuilletages et fibrations invariantes ». Thesis, Rennes 1, 2017. http://www.theses.fr/2017REN1S034/document.
Texte intégralThis thesis lies at the interface between algebraic geometry and dynamical systems. The goal is to analyse the dynamical behaviour of automorphisms (or, more generally, of birational transformations) of compact Kaehler manifolds having trivial first Chern class, in particular of hyperkaehler manifolds. I study the existence of geometric structures which are preserved by the dynamics, in particular fibrations and foliations, under some assumptions about the cohomological action of the transformation
Zhao, Sheng-Yuan. « Groupes kleiniens birationnels en dimension deux ». Thesis, Rennes 1, 2020. http://www.theses.fr/2020REN1S012.
Texte intégralIn this thesis I study a generalisation of Kleinian groups in the setting of complex algebraic geometry. The problem can also be seen as uniformization of projective varieties under an algebro-geometric hypothesis on the group of deck transformations. I give a classification of birational Kleinian groups in dimension two. It implements an interaction between birational transformations of surfaces,Kähler, groups, holomorphic foliations on complex surfaces, and Teichmüller spaces
Déserti, Julie. « Sur le groupe de Cremona : aspects algébriques etdynamiques ». Phd thesis, Université Rennes 1, 2006. http://tel.archives-ouvertes.fr/tel-00125492.
Texte intégralBeri, Pietro. « On birational transformations and automorphisms of some hyperkähler manifolds ». Thesis, Poitiers, 2020. http://www.theses.fr/2020POIT2267.
Texte intégralMy thesis work focuses on double EPW sextics, a family of hyperkähler manifolds which, in the general case, are equivalent by deformation to Hilbert's scheme of two points on a K3 surface. In particular I used the link that these manifolds have with Gushel-Mukai varieties, which are Fano varieties in a Grassmannian if their dimension is greater than two, K3 surfaces if their dimension is two.The first chapter contains some reminders of the theory of Pell's equations and lattices, which are fundamental for the study of hyperkähler manifolds. Then I recall the construction which associates a double covering to a sheaf on a normal variety.In the second chapter I discuss hyperkähler manifolds and describe their first properties; I also introduce the first case of hyperkähler manifold that has been studied, the K3 surfaces. This family of surfaces corresponds to the hyperkähler manifolds in dimension two.Furthermore, I briefly present some of the latest results in this field, in particular I define different module spaces of hyperkähler manifolds, and I describe the action of automorphism on the second cohomology group of a hyperkähler manifold.The tools introduced in the previous chapter do not provide a geometrical description of the action of automorphism on the manifold for the case of the Hilbert scheme of points on a general K3 surface. In the third chapter, I therefore introduce a geometrical description up to a certain deformation. This deformation takes into account the structure of Hilbert scheme. To do so, I introduce an isomorphism between a connected component of the module space of manifolds of type K3[n] with a polarization, and the module space of manifolds of the same type with an involution of which the rank of the invariant is one. This is a generalization of a result obtained by Boissière, An. Cattaneo, Markushevich and Sarti in dimension two. The first two parts of this chapter are a joint work with Alberto Cattaneo.In the fourth chapter, I define EPW sextics, using O'Grady's argument, which shows that a double covering of a EPW sextic in the general case is deformation equivalent to the Hilbert square of a K3 surface. Next, I present the Gushel-Mukai varieties, with emphasis on their connection with EPW sextics; this approach was introduced by O'Grady, continued by Iliev and Manivel and systematized by Kuznetsov and Debarre.In the fifth chapter, I use the tools introduced in the fourth chapter in the case where a K3 surface can be associated to a EPW sextic X. In this case I give explicit conditions on the Picard group of the surface for X to be a hyperkähler manifold. This allows to use Torelli's theorem for a K3 surface to demonstrate the existence of some automorphisms on X. I give some bounds on the structure of a subgroup of automorphisms of a sextic EPW under conditions of existence of a fixed point for the action of the group.Still in the case of the existence of a K3 surface associated with a EPW sextic X, I improve the bound obtained previously on the automorphisms of X, by giving an explicit link with the number of conics on the K3 surface. I show that the symplecticity of an automorphism on X depends on the symplecticity of a corresponding automorphism on the surface K3.The sixth chapter is a work in collaboration with Alberto Cattaneo. I study the group of birational automorphisms on Hilbert's scheme of points on a projective surface K3, in the generic case. This generalizes the result obtained in dimension two by Debarre and Macrì. Then I study the cases where there is a birational model where these automorphisms are regular. I describe in a geometrical way some involutions, whose existence has been proved before
Livres sur le sujet "Transformation birationnelle"
Cerveau, D. Transformations birationnelles de petit degré. Marseille, France : Société Mathématique de France, 2013.
Trouver le texte intégralGiraud, Georges. Sur une classe de groupes discontinus de transformations birationnelles quadratiques et sur les fonctions de trois variables independantes restant invariables par ces transformations. Paris : Gautheir-Villars, 1991.
Trouver le texte intégralMalet, Henri. Étude Géométrique Des Transformations Birationnelles Et Des Courbes Planes, Par Henri Malet. University of Michigan Library, 2006.
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