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An algebraic variety is a fundamental object in the field of algebraic geometry: it is a topological space whose points are roots of certain polynomial equations. There is a category of algebraic varieties and the morphisms are continuous maps that have additional structure. Agroup variety is a group object in the category of algebraic varieties. Given this data and today’s lecture, write down as much as possible about the definition of a group variety. A slightly different definition of “group variety” is given in Hartshorne’s Algebraic Geometry, in Exercise 3.21 of Chapter I. 1
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