Differential Bundles in Commutative Algebra and Algebraic Geometry
Theory and Applications of Categories, 2023 In this paper, we explain how the abstract notion of a differential bundle in a tangent category provides a new way of thinking about the category of modules over a commutative ring and its opposite category.
G. S. H. Cruttwell +1 more
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Poisson algebras via model theory and differential-algebraic geometry [PDF]
Journal of the European Mathematical Society, 2017 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.
Bell, Jason +3 more
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Bertini theorems for differential algebraic geometry [PDF]
Proceedings of the American Mathematical Society, 2016 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
James Freitag
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Algebraic geometry and local differential geometry [PDF]
Annales scientifiques de l'École normale supérieure, 1979 Phillip Griffiths, Joseph Harris
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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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Embedding Method by Real Numerical Algebraic Geometry for Structurally Unamenable Differential-Algebraic Equations [PDF]
Journal of Systems Science and Complexity, 2021 Existing structural analysis methods may fail to find all hidden constraints for a system of differential-algebraic equations with parameters if the system is structurally unamenable for certain values of the parameters.
Wenqiang Yang, Wenyuan Wu, Greg Reid
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Finiteness theorems on hypersurfaces in partial differential-algebraic geometry [PDF]
, 2017 James Freitag, Rahim Moosa
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Regularising Transformations for Complex Differential Equations with Movable Algebraic Singularities [PDF]
Mathematical physics, analysis and geometry, 2022 In a 1979 paper, Okamoto introduced the space of initial values for the six Painlevé equations and their associated Hamiltonian systems, showing that these define regular initial value problems at every point of an augmented phase space, a rational ...
T. Kecker, G. Filipuk
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Jacobian problems in differential equations and algebraic geometry [PDF]
, 1982 Gary H. Meisters
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The fundamental theorem of tropical partial differential algebraic geometry [PDF]
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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