Course Algebraic Geometry PDF
Classical algebraic geometry is the study of the sets of of simultaneous solutions of collections of polynomial equations in several variables with coefficients in an algebraically closed field. Such sets are called algebraic varieties. So eg the set of simultaneous solutions of the equations X²+Y²=0 , XY=0 is an algebraic variety.
Because they are so easy to define, algebraic varieties appear in almost every area of mathematics. They play a crucial role in number theory, in topology, in differential geometry and complex geometry (ie the theory of complex manifolds). When the base field is C, an algebraic variety defines a complex manifold provided it has ”no kinks” (we shall give a precise definition later).
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| Course Algebraic Geometry PDF |
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Download PDF 1: Course Algebraic Geometry : HERE
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