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The emphasis on algebraic surfaces—algebraic varieties of dimension two—followed on from an essentially complete geometric theory of algebraic curves (dimension 1). The position in around 1870 was that the curve theory had incorporated with Brill–Noether theory the Riemann–Roch theorem in all its refinements (via the detailed geometry of the theta-divisor).
The Veronese surface arises naturally in the study of conics.A conic is a degree 2 plane curve, thus defined by an equation: + + + + + = The pairing between coefficients (,,,,,) and variables (,,) is linear in coefficients and quadratic in the variables; the Veronese map makes it linear in the coefficients and linear in the monomials.
In mathematics, an algebraic surface is an algebraic variety of dimension two. In the case of geometry over the field of complex numbers , an algebraic surface has complex dimension two (as a complex manifold , when it is non-singular ) and so of dimension four as a smooth manifold .
Quotient surfaces, surfaces that are constructed as the orbit space of some other surface by the action of a finite group; examples include Kummer, Godeaux, Hopf, and Inoue surfaces; Zariski surfaces, surfaces in finite characteristic that admit a purely inseparable dominant rational map from the projective plane
An algebraic surface is an algebraic variety of dimension two. The Enriques-Kodaira classification gives an overview of the possibilities. Over the complex numbers, a non-singular algebraic surface is an example of a 4-manifold
Giacomo Albanese (11 July 1890 – 8 June 1947 [1]) was an Italian mathematician known for his work in algebraic geometry. He took a permanent position in the University of São Paulo, Brazil, in 1936.
Volume one. Algebraic exterior calculus and local differential properties], Istituto Nazionale di Alta Matematica (in Italian), Roma: Docet edizioni universitarie, p. 520, MR 0049646, Zbl 0045.19702. [8] Segre, Beniamino (1951b), Arithmetical Questions on Algebraic Varieties, London: The Athlone Press, pp. V+55, MR 0043498, Zbl 0042.15204. [9]
In algebraic geometry, a branch of mathematics, a Zariski surface is a surface over a field of characteristic p > 0 such that there is a dominant inseparable map of degree p from the projective plane to the surface. In particular, all Zariski surfaces are unirational.