Showing papers by "Zinovy Reichstein published in 2005"
TL;DR: In this paper, a numerical invariant of an algebraic group action called the canonical dimension is defined and applied to the problem of computing the minimal number of parameters required to define a generic hypersurface of degree d in P n - 1.
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TL;DR: In this paper, it was shown that the fixed elements for the natural GL_m-action on the universal division algebra UD(m,n) of m generic n x n matrices form a division subalgebra of degree n, assuming n >= 3 and 2 <= m <= n^2 - 2.
Abstract: We show that the fixed elements for the natural GL_m-action on the universal division algebra UD(m,n) of m generic n x n matrices form a division subalgebra of degree n, assuming n >= 3 and 2 <= m <= n^2 - 2. This allows us to describe the asymptotic behavior of the dimension of the space of SL_m-invariant homogeneous central polynomials p(X_1,...,X_m) for n x n matrices. Here the base field is assumed to be of characteristic zero.