Several Complex Variables
Several Complex Variables is a branch of mathematics that studies functions of multiple complex variables. It extends the concepts of complex analysis, which deals with functions of a single complex variable, to higher dimensions. This field explores properties such as holomorphicity, which refers to functions that are complex differentiable in a neighborhood of every point in their domain.
The study of several complex variables has applications in various areas, including algebraic geometry, partial differential equations, and theoretical physics. Key topics include complex manifolds, analytic varieties, and Cauchy-Riemann equations in higher dimensions. Researchers in this field aim to understand the intricate behavior of these functions and their geometric implications.