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arXiv · 1706.02533

The decomposition groups of plane conics and plane rational cubics

Tom Ducat·Isac Hedén·Susanna Zimmermann
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Abstract

The decomposition group of an irreducible plane curve $X\subset\mathbb P^2$ is the subgroup $\mathrm{Dec}(X)\subset\mathrm{Bir}(\mathbb P^2)$ of birational maps which restrict to a birational map of $X$. We show that $\mathrm{Dec}(X)$ is generated by its elements of degree $\leq2$ when $X$ is either a conic or rational cubic curve.

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Tom Ducat, Isac Hedén, Susanna Zimmermann. 2017-06-08. The decomposition groups of plane conics and plane rational cubics. https://arxiv.org/abs/1706.02533

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