Computer Aided Algebraic Geometry
Computer Aided Algebraic Geometry
Computer Aided Algebraic Geometry
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Surfaces of general type<br />
<strong>Computer</strong><br />
<strong>Aided</strong><br />
<strong>Algebraic</strong><br />
<strong>Geometry</strong><br />
R. Pignatelli<br />
Surfaces<br />
Invariants<br />
Quasi-étale<br />
quotients<br />
Definitions<br />
Computing<br />
invariants<br />
<strong>Computer</strong><br />
Calculations<br />
The Algorithms<br />
Classification<br />
Results<br />
The Enriques-Kodaira classification provides a relatively<br />
good understanding of the surfaces of special type, which<br />
are those with κ(S) < 2.<br />
Definition<br />
A surface is of general type if κ(S) = 2 (equiv.κ(S) ≥ 2) .<br />
Definition<br />
A surface is minimal if K S is nef, that is if the intersection of<br />
K S with any curve is nonnegative.<br />
Open<br />
Problems<br />
3 / 19
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