Thomas Ducat

Heilbronn Institute


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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