Zariski's Finiteness Theorem

In algebra, Zariski's finiteness theorem gives a positive answer to Hilbert's 14th problem for the polynomial ring in two variables, as a special case.http://aix1.uottawa.ca/~ddaigle/articles/H14survey.pdf Precisely, it states:
:Given a normal domain ''A'', finitely generated as an algebra over a field ''k'', if ''L'' is a subfield of the field of fractions of ''A'' containing ''k'' such that $\operatorname_k(L) \le 2$, then the ''k''-subalgebra $L \cap A$ is finitely generated.

References

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Hilbert's problems
Invariant theory
Commutative algebra

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