### The decomposition groups of plane conic and rational cubic curves

Linfoot Number Theory Seminar

15th November 2017, 11:00 am – 12:00 pm

Howard House, 4th Floor Seminar Room

The decomposition group of a plane curve C is the subgroup

of elements of the Cremona group which restrict to a birational map of

C. Hedén and Zimmermann proved that when C is a line then this group

is generated by linear maps and one elementary quadratic map

preserving C - an analogy of the Noether-Castelnuovo theorem for the

full Cremona group. Using this result we show that the decomposition

group is also generated by linear and quadratic maps when C is a conic

or rational cubic curve, but not in general for plane rational curves

of degree ≥4. This is joint work with Isac Hedén and Susanna

Zimmermann.

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