We show that the decomposition group of a line $L$ in the plane, i.e. the
subgroup of plane birational transformations that send $L$ to itself
birationally, is generated by its elements of degree 1 and one element of
degree 2, and that it does not decompose as a non-trivial amalgamated product.Comment: 15 pages, 7 figure

Hedén, Isac

Zimmermann, Susanna

English

arXiv

We show that the decomposition group of a line L in the plane, i.e. the subgroup of plane birational transformations that send L to itself birationally, is generated by its elements of degree 1 and one element of degree 2, and that it does not decompose as a non-trivial amalgamated product

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The decomposition group of a line in the plane

International audienceWe show that the decomposition group of a line L in the plane, i.e., the subgroup of plane birational transformations that send L to itself birationally, is generated by its elements of degree 1 and one element of degree 2, and that it does not decompose as a non-trivial amalgamated product

The decomposition group of a line in the plane

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