Introduction
Various approaches to classical TGD
Could one identify spacetime surfaces as zero loci for octonionic polynomials with real coefficients?
Topics to be discussed
Some basic notions, ideas, results, and conjectures of algebraic geometry
Algebraic varieties, curves and surfaces
About algebraic curves and surfaces
The notion of rational point and its generalization
About enumerative algebraic geometry
Some examples about enumerative algebraic geometry
About methods of algebraic enumerative geometry
GromowWitten invariants
RiemannRoch theorem
Does M^{8}H duality allow to use the machinery of algebraic geometry?
What does one really mean with M^{8}H duality?
Is the associativity of tangent/normal spaces really achieved?
M^{8}H duality: objections and challenges
Appendix: o^{2} as a simple test case
Option I: M^{4} is quaternionic
Option II: M^{4} is coquaternionic
