arXiv math/05041452005-04math.RTmath.AG

(Ir)Reducibility of some commuting varieties associated with involutions

Oksana Yakimova

备注：: New examples of reducible commuting varieties are added

英文摘要：

Here we prove that a commuting variety associated with a symmetric pair (g, g_0) is irreducible for (so_{n+m}, so_n + so_m) and reducible for (gl_{n+m}, {gl}_n + gl_m) with n>m, (so_{2n}, gl_n) with odd n, (E_6, {so}_{10} + k).

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