# name
A proof of Torelli's theorem for compact Riemann surfaces

# metadata.dc.description[].value
Treballs Finals de Grau de Matemàtiques, Facultat de Matemàtiques, Universitat de Barcelona, Any: 2025, Director: Juan Carlos Naranjo del Val

# metadata.dc.description.abstract[].value
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.

# metadata.dc.rights[].value
cc-by-nc-nd (c) Redouan Boukafri Itahriouan, 2025

# metadata.dc.source[].value
Treballs Finals de Grau (TFG) - Matemàtiques

# metadata.dc.title[].value
A proof of Torelli's theorem for compact Riemann surfaces