Arithmetic of plane Cremona transformations and the dimensions of transfinite heterotic string space-time

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 3–20. A firm algebraic geometrical justification is thus given not only for all the relevant dimensions of the classical theory, but also for the other two dimensions proposed by El Naschie, viz. the inverse of the quantum gravity coupling constant ( 42.36067977) and that of (one half of) the fine structure constant ( 68.54101967). A non-trivial coupling between the two El Naschie sequences is also revealed.