Algebraic Geometry Assignment Help

Algebraic geometry is one complex topic of geometry that deals with plane algebraic curves like hyperbolas, lines, circles, and parabolas; quartic and elliptic curves including Cassini ovals and lemniscates. It dates back to 5th century B.C. during the time of Hellenistic Greeks. The number theory can be combined with algebraic geometry for another active field of mathematics referred to as Arithmetic geometry. Here are some crucial topics that come under algebraic geometry.

• Algebraic Number Theory : It is the most important branch of number theory that uses the techniques of algebraic theory to analyze the rational number, integer, and its generalization.
• Analytic Number Theory : This branch of mathematics uses various mathematical methods to solve problems about integers. It is famous for its solutions on the prime number and additive number theory.
• Scheme Theory : In mathematics, scheme theory uses the methods of homological algebra and topology. In technical terms, it creates a strong connection between algebraic geometry and number theory.
• Sheaf Theory : Sheaf theory, in mathematics, is a primitive tool used for tracking data that is attached to the sets of topological space. Also, geometric structures can be expressed only in terms of sheaves.
• Algebraic Curves and Riemann Surfaces : In the complex analysis of mathematics, the algebraic curve is the set of points whose coordinates are zero of a polynomial in two variables. Whereas Riemann surface is a two-dimensional manifold that offers the simplification to other curves.