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Algebraic surfaces and 4-manifolds: Some conjectures and speculations

Algebraic surfaces and 4-manifolds: Some conjectures and speculations

Introduction.Since the time of Riemann, there has been a close interplay between the study of the geometry of complex algebraic curves (or, equivalently, compact Riemann surfaces) and the topology of 2-manifolds.These connections arise from the uniformization theorem, which asserts that every simply connected Riemann surface is conformally equivalent to either …