Rezidü teoremi ve düz projektif eğriler için açık bir dualite

The aim of this thesis is to present an explicit duality for smooth projective curves. More standard Serre duality achieves the final results exhibited in the thesis with far greater generality, using powerful homological machinery. The shortcom- ing of such methods, however, is that they do not yield an explicit dualizing sheaf but only show its existence. The general form of the treatment of the subject we follow was given by Serre in 1959 ([Ser]). A cornerstone of this treatment is the residue theorem, which essentially states that the sum of the residues for a given differential at all points of a regular projective curve is 0. Tate improved upon Serre?s treatement (in [Tat]), giving an elegant, characteristic independent proof of the residue theorem by defining residues in a novel way. Hence, our account gen- erally follows Tate, drawing parallels to Serre where appropriate (and occasionally to Chevalley?s 1951 work [Che] which contains some seeds of the ideas involved, al- beit from a purely algebraic viewpoint). Having developed duality, to demonstrate its power, we conclude the thesis with the proof of a form of the Riemann-Roch Theorem.