Teorema de Riemann-Roch

The Riemann-Roch theorem is a fundamental result in algebraic geometry that relates the number of independent functions (or "sections") that can be defined on a complex curve (a shape like a donut or a sphere) to its geometric properties, such as its shape and the points where functions can have poles or zeros. In essence, it provides a formula to calculate how many functions with certain behaviors exist on a curve, linking complex analysis, geometry, and topology. This theorem helps mathematicians understand the structure of curves and the functions defined on them.