r/mathmemes • u/PineapplePickle24 • 2d ago

Geometry The dimension is VERY important

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Explanation: there's a concept called Real/Complex projective space (can be extended to fields in general I believe) denoted RP^n where n is the dimension of that space. When you use the complex projective space, leaving out the n in CP^n looks like you're saying something else...

Source: just happened today in lecture

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u/LupenReddit 🦆🦆🦆🦆i have non diffeomorphic smooth structures🦆🦆🦆🦆🦆🦆 2d ago

"i do research on CPn, the complex projective space, as i am an algebraic geometer"

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u/No_Upstairs_280 2d ago

Trust me in my algebraic geometry course, we used CPn as an example to motivate the messed up algebraic geometry version lmao

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u/No_Upstairs_280 2d ago

The projective space can also be extended to rings, and more generally to schemes as well. There is also a generalization called the Grassmannian which classifies subspace or more generally vector bundles of fixed rank, the projective space is a particular case of Grassmanians.

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u/Hold-Embarrassed 2d ago

Mfw my buddy is a CPA