Weierstrass points

Weierstrass points are special points on a mathematical object called a Riemann surface (a shape that locally looks like a stretched-out sheet). At these points, the ways you can analyze functions—specifically, meromorphic functions—are more limited or unique compared to most other points. They can be thought of as "hot spots" where the usual behavior of functions exhibits exceptional properties, highlighting the underlying complex structure of the surface. These points are important in understanding the geometry and complex analysis of the surface, acting as key markers of its intrinsic features.