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Birational geometry is a field of algebraic geometry the goal of which is to determine when two algebraic varieties are isomorphic outside lower-dimensional subsets. This amounts to studying mappings that are given by rational functions rather than polynomials; the map may fail to be defined where the rational functions have poles.

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Integral graded algebra of finite type is approximable

The following is the definition of approximable algebra. An integral graded $K$-algebra $\oplus_{n\geqslant 0}B_n$ is said to be approximable if 1.$$rk_K(B_n)<+\infty,\forall n\in \mathbb{N}, $$and $$ …
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