  Let kK be the path algebra of the Kronecker quiver and consider the category
of finite dimensional right modules over kK (called Kronecker modules). We
prove that extensions of Kronecker modules are field independent up to Segre
classes, so they can be described purely combinatorially. We use in the proof
explicit descriptions of particular extensions and a variant of the well known
Green formula for Ringel-Hall numbers, valid over arbitrary fields. We end the
paper with some results on extensions of preinjective Kronecker modules,
involving the dominance ordering from partition combinatorics and its various
generalizations.
