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17 relations: Algebraic surface, Betti number, Birational geometry, Blowing up, Complex manifold, Complex projective space, Cremona group, Del Pezzo surface, Fake projective plane, Homogeneous coordinates, Mathematics, Projective geometry, Quadric, Rational surface, Riemann sphere, Toric variety, W. H. Freeman and Company.
Algebraic surface
In mathematics, an algebraic surface is an algebraic variety of dimension two.
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Betti number
In algebraic topology, the Betti numbers are used to distinguish topological spaces based on the connectivity of n-dimensional simplicial complexes.
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Birational geometry
In mathematics, birational geometry is a field of algebraic geometry the goal of which is to determine when two algebraic varieties are isomorphic outside lower-dimensional subsets.
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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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Complex manifold
In differential geometry, a complex manifold is a manifold with an atlas of charts to the open unit disk in Cn, such that the transition maps are holomorphic.
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Complex projective space
In mathematics, complex projective space is the projective space with respect to the field of complex numbers.
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Cremona group
In algebraic geometry, the Cremona group, introduced by, is the group of birational automorphisms of the n-dimensional projective space over a field k. It is denoted by Cr(Pn(k)) or Bir(Pn(k)) or Crn(k).
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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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Fake projective plane
In mathematics, a fake projective plane (or Mumford surface) is one of the 50 complex algebraic surfaces that have the same Betti numbers as the projective plane, but are not isomorphic to it.
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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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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Projective geometry
Projective geometry is a topic in mathematics.
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Quadric
In mathematics, a quadric or quadric surface (quadric hypersurface in higher dimensions), is a generalization of conic sections (ellipses, parabolas, and hyperbolas).
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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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Riemann sphere
In mathematics, the Riemann sphere, named after Bernhard Riemann, is a model of the extended complex plane, the complex plane plus a point at infinity.
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Toric variety
In algebraic geometry, a toric variety or torus embedding is an algebraic variety containing an algebraic torus as an open dense subset, such that the action of the torus on itself extends to the whole variety.
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