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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.
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