nprofile1qy2hwumn8ghj7un9d3shjtnddaehgu3wwp6kyqpqu9k7qvxzg5fk3cd3zqnqxu4czmrvjnn8zdrspqcgwcrnmz3rwwgsqzgt5c (nprofile…gt5c)
"could you elaborate on how projective geometry appears here?"
I wouldn't say "projective geometry", I'd say "projective algebraic geometry": the study of projective varieties, which are certain nice subspaces of projective space:
https://en.wikipedia.org/wiki/Projective_variety
It's a very long story, but I summarized it in my post (4/n).
An affine variety is just another way of talking about a commutative ring, namely the ring of regular functions on that variety. For a projective variety this fails, since there are usually very few regular functions on a projective variety.
This is why algebraic geometers turned to working with sheaves in the 1940s. They often study a projective variety by looking at the quasicoherent sheaves on that variety. These form a 2-rig, and this 2-rig has all the information you need.
Jim's idea is to simply work directly with the 2-rig. In many videos he's been developing algebraic geometry from this viewpoint.
John Carlos Baez /
npub17u…8pd6m
2025-01-11 21:34:24
in reply to nevent1q…0t4k
Author Public Key
npub17u6xav5rjq4d48fpcyy6j05rz2xelp7clnl8ptvpnval9tvmectqp8pd6mPublished at
2025-01-11 21:34:24Event JSON
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