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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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Question about valuation and blow up (a lemma in GIT book)

do you know how we cunstruct a blow up? for your first question blow up of affine $A$ at the ideal $I$ is covered by $$Spec(A[\frac{x^{r_0}\cdot y^{s_0}}{x^{r_i}\cdot y^{s_i}},...,\frac{x^{r_n}\cdot y …
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