Arithmetic of Plane Cremona Transformations and the Dimensions of Transfinite Heterotic String Space-Time

Details Arithmetic of Plane Cremona Transformations and the Dimensions of Transfinite Heterotic String Space-Time Arithmetic of Plane Cremona Transformations and the Dimensions of Transfinite Heterotic String Space-Time

2001-05-16

arxiv.org/abs/physics/0105049v1

ChaosSolitonsFractals13:1537-1540,2001

Physics

General Physics

4 pages, no figures, accepted in Chaos, Solitons & Fractals

Scientific paper

10.1016/S0960-0779(01)00125-4

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.

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