algebraic surface

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algebraic surface

[¦al·jə¦brā·ik ′sər·fəs]
(mathematics)
A subset S of a complex n-space which consists of the set of complex solutions of a system of polynomial equations in n variables such that S is a complex two-manifold in the neighborhood of most of its points.
References in periodicals archive ?
Artin, Some numerical criteria for contractability of curves on algebraic surfaces, Amer.
Fujita, Fractionally logarithmic canonical rings of algebraic surfaces, J.
I am interested in questions of enumerative geometry on algebraic surfaces S.
SILHOL, Real algebraic surfaces, Lecture Notes in Math.
SILHOL, Real algebraic surfaces with rational or elliptic fiberings, Math.
Automatic determination of algebraic surfaces as loci of points, Lecture Notes in Computer Science, 2657, Springer, 2003
Shigefumi Mori, 39, of Kyoto University, has devoted much of his career to pioneering methods of classifying certain kinds of surfaces defined by algebraic equations, thereby extending the classical theory of algebraic surfaces to three dimensions.
Using this result, new methods for blending several algebraic surfaces simultaneously are derived.
For an irreducible algebraic space curve C that is implicitly defined as the intersection of two algebraic surfaces, f(x, y, z) = 0 and g(x, y, z) = 0, there always exists a birational correspondence between the points of C and the points of an irreducible plane curve P, whose genus is the same as that of C.
Liedtke, Algebraic surfaces of general type with small [c.
Moreover, all known values of Seshadri constants on algebraic surfaces are rational.
As applications, we give some results supplementary to the theory of algebraic surfaces in arbitrary characteristic.