Results 11 to 20 of about 4,250 (281)
Bertini theorems for differential algebraic geometry [PDF]
Proceedings of the American Mathematical Society, 2023 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 Bertini’s theorem, namely that for an arbitrary geometrically irreducible differential algebraic ...
James Freitag
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On the Relationship Between Differential Algebra and Tropical Differential Algebraic Geometry [PDF]
, 2021 This paper presents the relationship between differential algebra and tropical differential algebraic geometry, mostly focusing on the existence problem of formal power series solutions for systems of polynomial ODE and PDE. Moreover, it improves an approximation theorem involved in the proof of the fundamental theorem of tropical differential ...
Boulier, François +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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Nonsmooth differential geometry and algebras of generalized functions [PDF]
Journal of Mathematical Analysis and Applications, 2004 17 pages, typos ...
Michael Kunzinger
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Noncommutative Differential Geometry of Generalized Weyl Algebras [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2016 Elements of noncommutative differential geometry of ${\mathbb Z}$-graded generalized Weyl algebras ${\mathcal A}(p;q)$ over the ring of polynomials in two variables and their zero-degree subalgebras ${\mathcal B}(p;q)$, which themselves are generalized Weyl algebras over the ring of polynomials in one variable, are discussed.
Tomasz Brzeziński
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Graded differential geometry of graded matrix algebras [PDF]
Journal of Mathematical Physics, 1999 We study the graded derivation-based noncommutative differential geometry of the Z2-graded algebra M(n|m) of complex (n+m)×(n+m)-matrices with the “usual block matrix grading” (for n≠m). Beside the (infinite-dimensional) algebra of graded forms, the graded Cartan calculus, graded symplectic structure, graded vector bundles, graded connections and ...
Grosse, H., Reiter, G.
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Differential algebra (contravariant analytic methods in differential geometry) [PDF]
Journal of Soviet Mathematics, 1980 The problems of developing the apparatus of differential-geometric investigations based on the calculus of differential operators on bundles of semiholonomic jets of Ehresmann are considered.
A. M. Vasil'ev
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Differential structures in algebraic geometry
, 2000 Cette thèse a pour objet d'une part l'étude de certaines structures différentielles sur les variétés algébriques complexes et d'autre part l'étude de faisceaux sur les hypersur-faces cubiques de l'espace projectif complexe de dimension quatre.Dans une première partie, nous donnons une description complète des structures de Poisson quasi-régulières non ...
Stéphane Druel
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Differential Geometry Revisited by Biquaternion Clifford Algebra [PDF]
, 2015 In the last century, differential geometry has been expressed within various calculi: vectors, tensors, spinors, exterior differential forms and recently Clifford algebras. Clifford algebras yield an excellent representation of the rotation group and of the Lorentz group which are the cornerstones of the theory of moving frames.
Girard, Patrick +4 more
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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. MacAdam previously showed that differential bundles in the tangent category of smooth manifolds are precisely smooth vector bundles.
Cruttwell, G. S. H. +1 more
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