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We give an introduction to algebraic geometry. Algebraic geometry is the study of the solution sets of polynomial equations (algebraic varieties) and has a long, rich history.
We begin by studying algebraic curves, before moving to higher dimensions.
We give a computational based approach to the fundamental notions of varieties. We shall use the freely available software Macaulay2 to see more involved examples than would be impossible by hand.
We will review the necessary preliminaries in topology and commutative algebra.
We'll use the following books.
Complex Algebraic Curves, F. Kirwan.
Algebraic Curves. An introduction to algebraic geometry, W. Fulton
Ideals, varieties and Algorithms, D. Cox, J. Little, D. O'Shea
Undergraduate algebraic geometry M. Ried
Helpful material
Visualisation of lines and conics in real projective space
Please follow this link to try Macaulay2 online. The tutorials found on the left hand side are a good warm up.
Here is a good graphing software to explore polynomial equations: Grapher.
Remarks on algebraic geometry, Cheltsov
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