A proof of Torelli's theorem for compact Riemann surfaces

Naranjo del Val, Juan CarlosBoukafri Itahriouan, Redouan2025-06-112025-06-112025-01-15https://hdl.handle.net/2445/221484Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2025, Director: Juan Carlos Naranjo del ValThe 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.63 p.application/pdfengcc-by-nc-nd (c) Redouan Boukafri Itahriouan, 2025http://creativecommons.org/licenses/by-nc-nd/3.0/es/Corbes modularsAutomorfismesFuncions thetaSuperfícies de RiemannTreballs de fi de grauModular curvesAutomorphismsTheta functionsRiemann surfacesBachelor's thesesA proof of Torelli's theorem for compact Riemann surfacesinfo:eu-repo/semantics/bachelorThesisinfo:eu-repo/semantics/openAccess