Question on projective variety

Dear Prof Kim.

In the Algebraic Geometry notes, we defined a Projective Algebraic Variety to be a subset of the projective space defined by the zeros of a homogeneous polynomial equation. Do we require the Algebraic set to be irreducible as well? and if so, why do we require this extra condition?

Thank you very much.

Acyr

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Because you know too much, you’re looking ahead already. We haven’t yet formally discussed the definition of a projective variety. Rather we’re just discussing examples. We’ll get to the issue of irreducibility and so on within a few weeks, and the question of the precisely correct definition.

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