  We continue study of some algebraic varieties (called resultantal varieties)
started in a paper of A. Grishkov, D. Logachev "Resultantal varieties related
to zeroes of L-functions of Carlitz modules". These varieties are related with
the Sylvester matrix for the resultant of two polynomials, from one side, and
with the L-functions of twisted Carlitz modules, from another side.
Surprisingly, these varieties are described in terms of finite weighted rooted
binary trees. We give a (conjecturally) complete description of them, we find
parametrizations of their irreducible components and their invariants: degrees,
multiplicities, Jordan forms, Galois actions. Proof of the fact that this
description is really complete is a subject of future research. Maybe a
generalization of these results will give us a solution of the problem of
boundedness of the analytic rank of twists of Carlitz modules.
