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Results tagged with birational-geometry
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user 134269
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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Isometry fixes ample class implies it is an automorphism?
My question is related to lemma 5.12 in ["Normal Subgroups in the Cremona Group"]. Let $h$ be a birational transformation of a projective surface $X$ and $[D']\in N^1(X)$ be an ample class. We define …
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Action of birational map $f$ on the divisor class of line $[H]$
In the paper "Normal Subgroups in the Cremona Group", it is stated that the induced isometry $f_{\ast}$ of $f\in J_d$, where $J_d$ denote the set of Jonquières transformations of degree $d$, satisfies …
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Non- simplicity of $\text{Bir}(\mathbb{P}_\mathbb{R}^2)$
In this paper: https://perso.univ-rennes1.fr/serge.cantat/Articles/nsgc-acta-c.pdf the authors said that their article 'directly implied' that $\text{Bir}(\mathbb{P}_\mathbb{R}^2)$ is not simple as w …
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Lifting of automorphism of rational surface to that on abelian variety
The paper I am referencing is "Normal Subgroups of the Cremona Group." https://arxiv.org/abs/1007.0895. In theorem 5.14, at the bottom of page 52, the author stated for the abelian surface $Y= \mathbb …
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