Roots of the affine Cremona group

Details Roots of the affine Cremona group Roots of the affine Cremona group

2010-10-19

arxiv.org/abs/1010.4034v1

Transformation groups, Vol. 16, No 4, 2011, pp. 1137-1142

Mathematics

Algebraic Geometry

4 pages

Scientific paper

10.1007/s00031-011-9140-y

Let k[x_1,...,x_n] be the polynomial algebra in n variables and let A^n=Spec
k[x_1,...,x_n]. In this note we show that the root vectors of the affine
Cremona group Aut(A^n) with respect to the diagonal torus are exactly the
locally nilpotent derivations x^a\times d/dx_i, where x^a is any monomial not
depending on x_i. This answers a question due to Popov.

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