File Name: ideals varieties and algorithms .zip
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Geometric objects can often be described as the solution sets of algebraic equations. Simple examples in three-dimensional space are curves like. In this course, we will investigate questions such as: How can one compute the equations for the intersection or union of two such objects? How can one determine whether two systems of algebraic equations describe the same geometric object? These are basic questions at the foundations of algebraic geometry.
At its heart, algebraic geometry is nothing more than a dictionary. Many theorems in the area simply involve taking properties of polynomial equations and translating them into properties of the geometric objects they describe. Other theorems take properties of well defined geometric objects and translate them into properties of their defining equations. Some of the complicated theorems involve bouncing back and forth between the two languages for a while. Many books on algebraic geometry spend their energy describing high-tech machines such as sheaves, schemes, and cohomology theories that have been developed in order to make the area as powerful as possible.
It seems that you're in Germany. We have a dedicated site for Germany. This text covers topics in algebraic geometry and commutative algebra with a strong perspective toward practical and computational aspects.
This text covers topics in algebraic geometry and commutative algebra with a strong perspective toward practical and computational aspects. The first four chapters form the core of the book.
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