  It is shown that the two sequences of characteristic dimensions of
transfinite heterotic string space-time found by El Naschie can be remarkably
well accounted for in terms of the arithmetic of self-conjugate homaloidal nets
of plane algebraic curves of orders 3 to 20. A firm algebraic geometrical
justification is thus given not only for all the relevant dimensions of the
classical theory, but also for other two dimensions proposed by El Naschie,
viz. the inverse of quantum gravity coupling constant (~42.36067977) and that
of (one half of) fine structure constant (~68.54101967). A non-trivial coupling
between the two El Naschie sequences is also revealed.
