• ALGEBRAIC GEOMETRY (STUDY OF STRUCTURE OF ALGEBRAIC GROUPS)

  
  
  

Reema Bishnoi

Abstract:
In algebraic geometry, the geometric properties of the solutions of systems of polynomial equations are examined using methods from algebra, geometry, and number theory. This robust framework allows us to understand and characterize the geometry of algebraic varieties, which are collections of points in a multi-dimensional space characterized by polynomial equations. The richness and diversity of algebraic geometry stem from its connections to other areas of mathematics, such as complex analysis and topology. One of the main focuses of algebraic geometry is algebraic varieties, which are geometric objects that satisfy a set of polynomial equations. These varieties can be described over a broad variety of fields, from the complex numbers to the real numbers to the finite fields. Discovering more about the dimensions, singular points, and crossings of these varieties is the goal of algebraic geometry.