Monday, January 22, 2007


Zariski surface

In algebraic geometry, a branch of mathematics, a Zariski surface is a surface over a field of characteristic p > 0 such there is a dominant inseparable map of degree p from the projective plane to the surface. In particular, all Zariski surfaces are unirational. They were named after Oscar Zariski who used them in 1958 to give examples of unirational surfaces in characteristic p > 0 that are not rational. (In characteristic 0 by contrast, Castelnuovo's theorem implies that all unirational surfaces are rational.) Zariski surfaces are birational to surfaces in affine 3-space A^3 defined by irreducible polynomials of the form
z^p = f(x, y).

This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Zariski surface". This entry is a fragment of a larger work. Link may die if entry is finally removed or merged.

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