Results 1 to 10 of about 6,777 (172)
Abelian reduction in differential-algebraic and bimeromorphic geometry [PDF]
Annales de l'Institut Fourier, 2022 A new tool for the model theory of differentially closed fields and of compact complex manifolds is here developed. In such settings, it is shown that a type internal to the field of constants (resp.
Rémi Jaoui, Rahim Moosa
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Algebraic geometry and local differential geometry [PDF]
Annales scientifiques de l'École normale supérieure, 1979 © Gauthier-Villars (Éditions scientifiques et médicales Elsevier), 1979, tous droits réservés. L’accès aux archives de la revue « Annales scientifiques de l’É.N.S. » (http://www. elsevier.com/locate/ansens) implique l’accord avec les conditions générales
P. Griffiths, J. Harris
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Finiteness theorems on hypersurfaces in partial differential-algebraic geometry [PDF]
Advances in Mathematics, 2016 Hrushovski's generalization and application of [Jouanolou, "Hypersurfaces solutions d'une quation de Pfaff analytique", Mathematische Annalen, 232 (3):239--245, 1978] is here refined and extended to the partial differential setting with possibly nonconstant coefficient fields. In particular, it is shown that if $X$ is a differential-algebraic variety
J. Freitag, Rahim Moosa
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Poisson algebras via model theory and differential-algebraic geometry [PDF]
Journal of the European Mathematical Society, 2014 Brown and Gordon asked whether the Poisson Dixmier-Moeglin equivalence holds for any complex affine Poisson algebra; that is, whether the sets of Poisson rational ideals, Poisson primitive ideals, and Poisson locally closed ideals coincide.
J. Bell +3 more
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Algebraic characterizations in complex differential geometry [PDF]
Transactions of the American Mathematical Society, 1935 1. In the treatment of differential geometry from the modern invariantive standpoint it is usually unnecessary that the coordinates and the functions which define the structure of the space under consideration be real quantities. Adopting the more general hypothesis of complex coordinates and structure functions we arrive at the concept of generalized ...
T. Y. Thomas
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Differential algebras in non-commutative geometry [PDF]
Journal of Geometry and Physics, 1995 We discuss the differential algebras used in Connes' approach to Yang-Mills theories with spontaneous symmetry breaking. These differential algebras generated by algebras of the form functions $\otimes$ matrix are shown to be skew tensorproducts of differential forms with a specific matrix algebra.
Wolfgang Kalau +3 more
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Nonassociative algebras: a framework for differential geometry [PDF]
International Journal of Mathematics and Mathematical Sciences, 2003 A nonassociative algebra endowed with a Lie bracket, called a torsion algebra, is viewed as an algebraic analog of a manifold with an affine connection. Its elements are interpreted as vector fields and its multiplication is interpreted as a connection. This provides a framework for differential geometry on a formal manifold with a formal connection. A
Lucian M. Ionescu
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The fundamental theorem of tropical partial differential algebraic geometry [PDF]
Proceedings of the 45th International Symposium on Symbolic and Algebraic Computation, 2020 Tropical Differential Algebraic Geometry considers difficult or even intractable problems in Differential Equations and tries to extract information on their solutions from a restricted structure of the input.
Sebastian Falkensteiner +5 more
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The Fundamental Theorem of Tropical Differential Algebraic Geometry [PDF]
Pacific Journal of Mathematics, 2015 Let $I$ be an ideal of the ring of Laurent polynomials $K[x_1^{\pm1},\ldots,x_n^{\pm1}]$ with coefficients in a real-valued field $(K,v)$. The fundamental theorem of tropical algebraic geometry states the equality $\text{trop}(V(I))=V(\text{trop}(I ...
F. Aroca +2 more
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Bertini theorems for differential algebraic geometry [PDF]
Proceedings of the American Mathematical Society, 2012 We study intersection theory for differential algebraic varieties. Particularly, we study families of differential hypersurface sections of arbitrary affine differential algebraic varieties over a differential field. We prove the differential analogue of
J. Freitag
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