Introduction

1. Various approaches to classical TGD

2. Could one identify space-time surfaces as zero loci for octonionic polynomials with real coefficients?

3. Topics to be discussed

Some basic notions, ideas, results, and conjectures of algebraic geometry

1. Algebraic varieties, curves and surfaces

2. About algebraic curves and surfaces

3. The notion of rational point and its generalization

About enumerative algebraic geometry

1. Some examples about enumerative algebraic geometry

2. About methods of algebraic enumerative geometry

3. Gromow-Witten invariants

4. Riemann-Roch theorem

Does M⁸-H duality allow to use the machinery of algebraic geometry?

1. What does one really mean with M⁸-H duality?

2. Is the associativity of tangent-/normal spaces really achieved?

3. M⁸-H duality: objections and challenges

Appendix: o² as a simple test case

1. Option I: M⁴ is quaternionic

2. Option II: M⁴ is co-quaternionic