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37 relations: Alfred Clebsch, Algebraic geometry, Algebraic surface, Algebraically closed field, Bitangents of a quartic, Blowing up, Brane, Cambridge University Press, Cayley's nodal cubic surface, Clebsch surface, Del Pezzo surface, E6 (mathematics), Exceptional divisor, Fermat cubic, Fundamental representation, General position, Homogeneous coordinates, Homogeneous polynomial, M-theory, McKay graph, Oxford University Press, Philosophical Transactions of the Royal Society, Polynomial, Projective plane, Projective space, Projective variety, Quaternary cubic, Rational surface, Schläfli double six, Singularity (mathematics), Smooth scheme, Springer Science+Business Media, Torus, U-duality, Vladimir Arnold, Weyl group, Wolfram Demonstrations Project.
Alfred Clebsch
Rudolf Friedrich Alfred Clebsch (19 January 1833 – 7 November 1872) was a German mathematician who made important contributions to algebraic geometry and invariant theory.
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Algebraic geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.
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Algebraic surface
In mathematics, an algebraic surface is an algebraic variety of dimension two.
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Algebraically closed field
In abstract algebra, an algebraically closed field F contains a root for every non-constant polynomial in F, the ring of polynomials in the variable x with coefficients in F.
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Bitangents of a quartic
In the theory of algebraic plane curves, a general quartic plane curve has 28 bitangent lines, lines that are tangent to the curve in two places.
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Blowing up
In mathematics, blowing up or blowup is a type of geometric transformation which replaces a subspace of a given space with all the directions pointing out of that subspace.
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Brane
In string theory and related theories such as supergravity theories, a brane is a physical object that generalizes the notion of a point particle to higher dimensions.
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Cambridge University Press
Cambridge University Press (CUP) is the publishing business of the University of Cambridge.
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Cayley's nodal cubic surface
In algebraic geometry, the Cayley surface, named after Arthur Cayley, is a cubic nodal surface in 3-dimensional projective space with four conical points.
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Clebsch surface
In mathematics, the Clebsch diagonal cubic surface, or Klein's icosahedral cubic surface, is a non-singular cubic surface, studied by and, all of whose 27 exceptional lines can be defined over the real numbers.
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Del Pezzo surface
In mathematics, a del Pezzo surface or Fano surface is a two-dimensional Fano variety, in other words a non-singular projective algebraic surface with ample anticanonical divisor class.
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E6 (mathematics)
In mathematics, E6 is the name of some closely related Lie groups, linear algebraic groups or their Lie algebras \mathfrak_6, all of which have dimension 78; the same notation E6 is used for the corresponding root lattice, which has rank 6.
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Exceptional divisor
In mathematics, specifically algebraic geometry, an exceptional divisor for a regular map of varieties is a kind of 'large' subvariety of X which is 'crushed' by f, in a certain definite sense.
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Fermat cubic
In geometry, the Fermat cubic, named after Pierre de Fermat, is a surface defined by Methods of algebraic geometry provide the following parameterization of Fermat's cubic: In projective space the Fermat cubic is given by The 27 lines lying on the Fermat cubic are easy to describe explicitly: they are the 9 lines of the form (w: aw: y: by) where a and b are fixed numbers with cube −1, and their 18 conjugates under permutations of coordinates.
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Fundamental representation
In representation theory of Lie groups and Lie algebras, a fundamental representation is an irreducible finite-dimensional representation of a semisimple Lie group or Lie algebra whose highest weight is a fundamental weight.
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General position
In algebraic geometry and computational geometry, general position is a notion of genericity for a set of points, or other geometric objects.
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Homogeneous coordinates
In mathematics, homogeneous coordinates or projective coordinates, introduced by August Ferdinand Möbius in his 1827 work Der barycentrische Calcül, are a system of coordinates used in projective geometry, as Cartesian coordinates are used in Euclidean geometry.
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Homogeneous polynomial
In mathematics, a homogeneous polynomial is a polynomial whose nonzero terms all have the same degree.
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M-theory
M-theory is a theory in physics that unifies all consistent versions of superstring theory.
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McKay graph
In mathematics, the McKay graph of a finite-dimensional representation V of a finite group G is a weighted quiver encoding the structure of the representation theory of G. Each node represents an irreducible representation of G. If \chi_i, \chi_j are irreducible representations of G then there is an arrow from \chi_i to \chi_j if and only if \chi_j is a constituent of the tensor product V\otimes\chi_i.
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Oxford University Press
Oxford University Press (OUP) is the largest university press in the world, and the second oldest after Cambridge University Press.
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Philosophical Transactions of the Royal Society
Philosophical Transactions, titled Philosophical Transactions of the Royal Society (often abbreviated as Phil. Trans.) from 1776, is a scientific journal published by the Royal Society.
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Polynomial
In mathematics, a polynomial is an expression consisting of variables (also called indeterminates) and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponents of variables.
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Projective plane
In mathematics, a projective plane is a geometric structure that extends the concept of a plane.
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Projective space
In mathematics, a projective space can be thought of as the set of lines through the origin of a vector space V. The cases when and are the real projective line and the real projective plane, respectively, where R denotes the field of real numbers, R2 denotes ordered pairs of real numbers, and R3 denotes ordered triplets of real numbers.
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Projective variety
In algebraic geometry, a projective variety over an algebraically closed field k is a subset of some projective ''n''-space Pn over k that is the zero-locus of some finite family of homogeneous polynomials of n + 1 variables with coefficients in k, that generate a prime ideal, the defining ideal of the variety.
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Quaternary cubic
In mathematics, a quaternary cubic form is a degree 3 homogeneous polynomial in four variables.
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Rational surface
In algebraic geometry, a branch of mathematics, a rational surface is a surface birationally equivalent to the projective plane, or in other words a rational variety of dimension two.
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Schläfli double six
In geometry, the Schläfli double six is a configuration of 30 points and 12 lines, introduced by.
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Singularity (mathematics)
In mathematics, a singularity is in general a point at which a given mathematical object is not defined, or a point of an exceptional set where it fails to be well-behaved in some particular way, such as differentiability.
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Smooth scheme
In algebraic geometry, a smooth scheme over a field is a scheme which is well approximated by affine space near any point.
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Springer Science+Business Media
Springer Science+Business Media or Springer, part of Springer Nature since 2015, is a global publishing company that publishes books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.
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Torus
In geometry, a torus (plural tori) is a surface of revolution generated by revolving a circle in three-dimensional space about an axis coplanar with the circle.
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U-duality
In physics, U-duality (short for unified duality) is a symmetry of string theory or M-theory combining S-duality and T-duality transformations.
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Vladimir Arnold
Vladimir Igorevich Arnold (alternative spelling Arnol'd, Влади́мир И́горевич Арно́льд, 12 June 1937 – 3 June 2010) was a Soviet and Russian mathematician.
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Weyl group
In mathematics, in particular the theory of Lie algebras, the Weyl group of a root system Φ is a subgroup of the isometry group of the root system.
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Wolfram Demonstrations Project
The Wolfram Demonstrations Project is an organized, open-source collection of small (or medium-size) interactive programs called Demonstrations, which are meant to visually and interactively represent ideas from a range of fields.
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27 lines on a cubic surface, Cayley-Salmon theorem, Cayley–Salmon theorem, Cayley−Salmon theorem, Eckardt point.
References
[1] https://en.wikipedia.org/wiki/Cubic_surface
