Algebraic geometry

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Algebraic geometry is a branch of mathematics studying polynomial equations. Modern algebraic geometry is based on more abstract techniques of abstract algebra, especially commutative algebra, with the language and the problems of geometry.


Algebraic geometry occupies a central place in modern mathematics. The concepts it uses connects it to such diverse fields as complex analysis, topology and number theory. At the start, algebraic geometry was about studying systems of polynomial equations in several variables. Algebraic geometry starts at the point where equation solving leaves off: In many cases, finding the properties all the solutions a given set of equations have is more important than finding a particular solution: this leads into some of the deepest areas in all of mathematics, both conceptually and in terms of technique.


  • A large part of singularity theory is devoted to the singularities of algebraic varieties.
  • When computers became more common, a field named 'computational algebraic geomery' developed. It looks at intersection of algebraic geometry and computer algebra. It is concerned with the development of algorithms and software for studying and finding the properties of explicitly given algebraic varieties.
