### Does M8-H Duality Reduce Classical TGD to Octonionic Algebraic Geometry? (Part I)

#### Abstract

TGD leads to several proposals for the exact solution of field equations defining space-time surfaces as preferred extremals of twistor lift of Kahler action. So called *M ^{8}-H* duality is one of these approaches. The beauty of

*M*duality is that it could reduce classical TGD to algebraic geometry and would immediately provide deep insights to cognitive representation identified as sets of rational points of these surfaces.

^{8}-HIn part I of this two-part article, I shall consider the following topics: (1) Basic notions of algebraic geometry such as algebraic variety, surface, and curve; (2) Redution of *M ^{8}-H* duality to octonionic algebraic geometry; (3) Products of polynomials as correlates for free many-particle states with interactions described by added interaction polynomial; (4) Discussions of the octonionic polynomials with real coefficients giving rise to associative (co-associative) surfaces as the zero loci of their real part ; (5) Generalization of Cauchy-Riemann conditions for complex analytic functions to quaternions and octonions; and (6) Polynomials with universal dynamics of criticality.