The decomposition groups of plane conics and plane rational cubics

2017/06/08 by Tom Ducat, Ducat, Tom, Isac Hedén +3
Mathematics · #14E07 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14E07

paper · pdf · doi:10.48550/arxiv.1706.02533

12 pages, 6 figures. Comments are welcome

arxiv created 2017/06/08 · arxiv updated 2017/06/09

Abstract

The decomposition group of an irreducible plane curve X⊂\mathbb P² is the subgroup Dec(X)\subsetBir(\mathbb P²) of birational maps which restrict to a birational map of X. We show that Dec(X) is generated by its elements of degree ≤2 when X is either a conic or rational cubic curve.

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