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    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeDec 13th 2010

    started a stub for projective space

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeDec 13th 2010

    Added the first part of the proof that a \mathbb{Z}-grading on a commutative ring RR is the same as a 𝔾 m\mathbb{G}_m-action on SpecRSpec R. (All a bit rough for the time being.)

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeDec 14th 2010
    • (edited Dec 14th 2010)

    added to projective space the remainder of the proof that 𝔾\mathbb{G}-actions on SpecRSpec R are equivalent to \mathbb{Z}-gradings of RR.

    (I guess I should move that elsewhere.)

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJun 11th 2017
    • (edited Jun 11th 2017)

    I have spelled out how real and projective space become topological manifolds and smooth manifolds, here.

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeJun 12th 2017

    I have filled in full details in the proof of the CW-structure at complex projective space. Then I copied this over also to Projective space – Examples – Real and complex projective space, so that the discussion there is now a self-contained proof of the manifold structure on real/complex projective space.

    • CommentRowNumber6.
    • CommentAuthorUrs
    • CommentTimeAug 9th 2017

    Among the list of elementary facts, the statement that S nP nS^n \to \mathbb{R}P^n is locally trivial had been missing. For completeness, have now included statement and proof here.