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Please use this identifier to cite or link to this item: https://hdl.handle.net/2445/221484
A proof of Torelli's theorem for compact Riemann surfaces
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The aim of this work is to explore algebraic geometry and its connections with complex analysis and topology through a proof of Torelli’s Theorem for compact Riemann surfaces. The theorem asserts that a compact Riemann surface is uniquely determined by its Jacobian and theta divisor. To establish this result, we first develop the theoretical framework, beginning with differential 1-forms and the concept of divisors. We then prove the Riemann-Roch Theorem, followed by a study of the theory of Jacobians via the Abel Theorem. These tools and results finally culminate in the proof of Torelli’s Theorem.
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Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2025, Director: Juan Carlos Naranjo del Val
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BOUKAFRI ITAHRIOUAN, Redouan. A proof of Torelli's theorem for compact Riemann surfaces. [consulted: 8 of August of 2026]. Available at: https://hdl.handle.net/2445/221484