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Results tagged with birational-geometry
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user 31524
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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Crepant Birational Map on the Blow-up
Let $ f: \mathbb{P}^n \dashrightarrow (\mathbb{P}^1)^n , [x_0:\dots :x_n] \mapsto ([x_0,x_1],[x_0,x_2], \dots ,[x_0,x_n])$ a birational map.
In particular, if $X$ is the blow-up of $\mathbb{P}^n$ at …
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Crepant Birational Map
Let $ f: \mathbb{P}^n \dashrightarrow (\mathbb{P}^1)^n , [x_0:\dots :x_n] \mapsto ([x_0,x_1],[x_0,x_2], \dots ,[x_0,x_n])$ a birational map.
Is $f$ a Crepant birational map?
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Is always a Crepant birational map between smooth varieties a small modification
Lemma: A crepant birational map between quasi-projective normal varieties with only terminal singularities is in fact small modifitacions, i.e. isomorphism in codimension 1.
So, if $f:X\dashrightarro …
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