ERRATUM TO INTRINSIC STRATIFICATION OF ANALYTIC VARIETIES
FRANC¸ OIS TREVES
As stated Theorem 2 is erroneous. The correct statement is the following: Theorem 2. Let V be an analytic subvariety of the analytic manifold M. The Nagano foliation of V has the following property:
If two distinct Nagano leaves of V in M, L1, L2, are such that L1∩ L2 6= ∅
then dim L1 < dim L2 and L1 ⊂ ∂L2. Furthermore, the tangent bundle T L1 is
contained in the closure T L2 of T L2 in T M.
The Nagano foliation is a stratification if and only if it is locally finite. But this might not be the case (contrary to the statement in the article) as shown in the following.
Example 1. Take V =x ∈ K3; x
1x2(x1− x2) (x1− x2x3) = 0 , K = R or C, a
version of the so-called four moving lines in C2. If x
1= x2= 0, x3(x3− 1) 6= 0, the
Lie algebra gx(V ) is generated by the radial vector x1∂x∂
1 + x2
∂
∂x2 in the (x1, x2
)-plane, implying that every such point x is a (zero-dimensional) Nagano leaf.
Bruno Pini Mathematical Analysis Seminar, Vol. 1 (2013) p. 84 Dipartimento di Matematica, Universit`a di Bologna
ISSN 2240-2829.
