143 research outputs found
Intrinsic palindromic numbers
We introduce a notion of palindromicity of a natural number which is
independent of the base. We study the existence and density of palindromic and
multiple palindromic numbers, and we raise several related questions.Comment: 6 pages, Latex2
Corrigendum for "A geometric proof of the Karpelevich-Mostow theorem"
Corollary 2.3 in our paper "A geometric proof of the Karpelevich-Mostow
theorem", Bull. Lond. Math. Soc. 41 (2009), no. 4, 634-638, is false. Here we
give a counterexample and show how to avoid the use of this corollary to give a
simpler proof of Karpelevich-Mostow theorem. We also include a short discussion
of the original proof by Karpelevich
Mok's characteristic varieties and the normal holonomy group
In this paper we complete the study of the normal holonomy groups of complex
submanifolds (non nec. complete) of Cn or CPn. We show that irreducible but non
transitive normal holonomies are exactly the Hermitian s-representations of
[CD09, Table 1] (see Corollary 1.1). For each one of them we construct a non
necessarily complete complex submanifold whose normal holonomy is the
prescribed s-representation. We also show that if the submanifold has
irreducible non transitive normal holonomy then it is an open subset of the
smooth part of one of the characteristic varieties studied by N. Mok in his
work about rigidity of locally symmetric spaces. Finally, we prove that if the
action of the normal holonomy group of a projective submanifold is reducible
then the submanifold is an open subset of the smooth part of a so called join,
i.e. the union of the lines joining two projective submanifolds
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