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- W1639097888 abstract "The $n$-dimensional affine group over the integers is the group $mathcal G_n$ of all affinities on $mathbb R^{n}$ which leave the lattice $ mathbb Z^{n}$ invariant. $mathcal G_n$ yields a geometry in the classical sense of the Erlangen Program. In this paper we construct a $mathcal G_n$-invariant measure on rational polyhedra in $mathbb R^n$, i.e., finite unions of simplexes with rational vertices in $mathbb R^n$, and prove its uniqueness. Our main tool is given by the Morelli-W{l}odarczyk factorization of birational toric maps in blow-ups and blow-downs (solution of the weak Oda conjecture)." @default.
- W1639097888 created "2016-06-24" @default.
- W1639097888 creator A5069739656 @default.
- W1639097888 date "2011-02-04" @default.
- W1639097888 modified "2023-09-27" @default.
- W1639097888 title "Measure theory in the geometry of $GL(n,mathbb Z) ltimes mathbb Z^{n}$" @default.
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- W1639097888 hasPublicationYear "2011" @default.
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