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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.

2 votes

A variant on the Fujita invariant

Here is an expansion on my comment. For a field $K$, let $X$ be a normal projective $K$-variety, let $\mathscr{L}$ be a big line bundle on $X$, and let $D$ be a nonzero effective Cartier divisor on $X …
Jackson Morrow's user avatar