User:AGBlgr/sandbox

Need a parent article named 'Affine algberaic geometry' to disambiguate it from just commutative algebra. It should showcase the most important subclass namely 'Affine algebraic surfaces'. This has a grand parent named 'Open algberaic surfaces' which should detail relevant theory.

Techniques: 1. purely algebraic (this is a manipulation of polynomials) and thus is a part of commutative algebra in a way 2. geometric - this studies fibrations on such a surface to glean more information, also the study of various invariants like Pic, ML-invariant, K-theory, A1-homotopy etc comes here. 3. Global geometric: the open surface theory, Iitaka philosophy, birational geometry of pairs. 4. Topological: fundamental group, both at finite and infinity; Issues of contractibility, (co)homology exact sequence of pair with snc divisor at infinity using various dualities especially Lefschetz duality. 5. Connections to other subjects: first is commalg, second is 3-dim topology and knot theory, A1-homotopy theory which is newly emerging, algebraic group actions (linearizations), singularities, char p theory. 6. Main questions motivating the subject: show like an expanding sphere with central questions at center, this should also serve as a vista of the subject. 7. Conjectural or speculative connections with other subjects: