Here by "surface" I mean a projective variety of dimension 2 (over an algebraically closed field k, as in Ch.1 of Hartshorne).
My question is:
Given a positive integer n >0, can we define a (possibly singular) surface S in n-dimensional projective space P^n, such that S does not admit an embedding into any P^m for m < n ?
That is, I am asking for a constructive proof, an effective algorithm taking as input n, that generates the set of homogenous polynomials defining such a surface.
How does this relate to the number and degrees of the homogenous polynomials required to define S ?
Unless you are directly interested in number theory, does it make much sense to do algebraic geometry independently of complex analytic geometry and complex analysis in several variables ?
- Badges
- Science topic
- Similar topics
- Computer Communications (Networks)
- Simulators