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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. Rational surfaces are the simplest of the 10 or so classes of surface in the Enriques–Kodaira classification of complex surfaces,
and were the first surfaces to be investigated.
==Structure==
Every non-singular rational surface can be obtained by repeatedly blowing up a minimal rational surface. The minimal rational surfaces are the projective plane and the Hirzebruch surfaces Σ''r'' for ''r'' = 0 or ''r'' ≥ 2.
Invariants: The plurigenera are all 0 and the fundamental group is trivial.
Hodge diamond:
where ''n'' is 0 for the projective plane, and 1 for Hirzebruch surfaces
and greater than 1 for other rational surfaces.
The Picard group is the odd unimodular lattice I1,''n'', except for the Hirzebruch surfaces Σ2''m'' when it is the even unimodular lattice II1,1.
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