Results 71 to 80 of about 164,410 (186)

Completeness in partial differential algebraic geometry

Journal of Algebra, 2014
This paper studies various aspects of complete differential algebraic varieties. The setting is the following, introduced by Kolchin. If \(F\) is a field of characteristic \(0\) equipped with \(m\) commuting derivations, then one has the notion of \textit{differential algebraic varieties} over \(F\). For simplicity, we fix a \textit{universal domain} \(
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Scattering equations: from projective spaces to tropical grassmannians

Journal of High Energy Physics, 2019
We introduce a natural generalization of the scattering equations, which connect the space of Mandelstam invariants to that of points on ℂℙ1, to higher-dimensional projective spaces ℂℙ k − 1.
Freddy Cachazo, Nick Early, Alfredo Guevara, Sebastian Mizera   +3 more
doaj   +1 more source

Special geometry on the 101 dimesional moduli space of the quintic threefold

Journal of High Energy Physics, 2018
A new method for explicit computation of the CY moduli space metric was proposed by the authors recently. The method makes use of the connection of the moduli space with a certain Frobenius algebra.
Konstantin Aleshkin, Alexander Belavin
doaj   +1 more source

Lectures on Graded Differential Algebras and Noncommutative Geometry [PDF]

, 2001
These notes contain a survey of some aspects of the theory of graded differential algebras and of noncommutative differential calculi as well as of some applications connected with physics. They also give a description of several new developments.
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Note on the Labelled tree graphs

Journal of High Energy Physics, 2020
In the CHY-frame for the tree-level amplitudes, the bi-adjoint scalar theory has played a fundamental role because it gives the on-shell Feynman diagrams for all other theories.
Bo Feng, Yaobo Zhang
doaj   +1 more source

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, Clarysse, Patrick, Pujol, Romaric, Wang, Liang, Delachartre, Philippe   +4 more
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Algebraic geometry and local differential geometry [PDF]

Annales scientifiques de l'École normale supérieure, 1979
Griffiths, Phillip, Harris, Joseph
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The CEGM NLSM

Journal of High Energy Physics
Studying quantum field theories through geometric principles has revealed deep connections between physics and mathematics, including the discovery by Cachazo, Early, Guevara and Mizera (CEGM) of a generalization of biadjoint scalar amplitudes.
Nick Early
doaj   +1 more source

Extreme 5-dimensional black holes with SU(2)-symmetric horizons

Journal of High Energy Physics
We show that the near horizon geometry of 5-dimensional extreme (i.e., degenerate) stationary vacuum black holes, with or without cosmological constant, whose event horizons exhibit SU(2) symmetry must be that of a Berger sphere.
Eric Bahuaud, Sharmila Gunasekaran, Hari K Kunduri, Eric Woolgar   +3 more
doaj   +1 more source

On the classical geometry of embedded surfaces in terms of Poisson brackets

, 2010
We consider surfaces embedded in a Riemannian manifold of arbitrary dimension and prove that many aspects of their differential geometry can be expressed in terms of a Poisson algebraic structure on the space of smooth functions of the surface.
Arnlind, Joakim, Hoppe, Jens, Huisken, Gerhard   +2 more
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