Elementary Algebraic Geometry

The present small book offers a nice introduction to algebraic geometry, based on an elementary algebraic level, without the use of sheaf or cohomology theory. There are chapters on affine and projective varieties, their smooth points and their dimension. Special attention is paid to plane cubic curves, their classification, group structure and multiplicity of their intersections. The second topic treated in the book is a study of cubic surfaces, its rationality and existence of lines on a cubic surface. The last chapter is an introduction to the theory of curves in projective planes, divisors and the Bezout theorem. Linear systems of curves and their projective embeddings are described here. At the end of each chapter, there are exercises of different level. At the end of the book, the reader can find a short bibliography on commutative algebra and algebraic geometry recommended for further study. The book is nicely written and can be recommended to anybody interested in basic algebraic geometry.

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