Algebraic Geometry

Description: Flat surfaces come in two distinct forms. Firstly, they can be portrayed as polygons with paired parallel edges and vertices glued to create conical points. Secondly, they can emerge from surface differentials, with the orders of zeros determining the angles of these conical points. Modifying the size of specific regions on a flat surface results in various limit surfaces, which fill the parameter space boundary of flat surfaces. These characteristics and attributes of flat surfaces render them a focal point of research, drawing the interest of scholars from diverse fields such as algebraic geometry, analytic geometry, arithmetic geometry, combinatorics, dynamics, hyperbolic geometry, topology, and mathematical physics.