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nLab > Latest Changes: K3 surface

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  1.  
    • CommentRowNumber1.
    • CommentAuthorUrs
    • CommentTimeOct 26th 2018
    • (edited Oct 26th 2018)

    starting to collect references on string/M-theory compactifications on K3-compactifications (here). Am also touching related entries such as Moonshine etc.

    diff, v14, current

    • CommentRowNumber2.
    • CommentAuthorUrs
    • CommentTimeOct 26th 2018

    added statement of the integral cohomology in all degrees, with pointer to a proof

    diff, v17, current

    • CommentRowNumber3.
    • CommentAuthorUrs
    • CommentTimeNov 11th 2019

    added statement of a few characteristic classes of K3K3 and of K3×K3K3 \times K3 (here)

    diff, v24, current

    • CommentRowNumber4.
    • CommentAuthorUrs
    • CommentTimeJun 5th 2020

    added pointer to today’s

    diff, v30, current

    • CommentRowNumber5.
    • CommentAuthorUrs
    • CommentTimeNov 20th 2020

    added statement of SU-bordism class (here)

    diff, v32, current

    • CommentRowNumber6.
    • CommentAuthorJohn Baez
    • CommentTimeMar 31st 2024
    • (edited Mar 31st 2024)

    The first sentence of the article defined a K3 surface to be a Calabi-Yau variety of dimension 22, which was wrong: we also need the condition H 1(X,𝒪 X)=0H^1(X, \mathcal{O}_X)=0, which appeared later. I fixed it.

    diff, v39, current

    • CommentRowNumber7.
    • CommentAuthorJohn Baez
    • CommentTimeMar 31st 2024

    I won’t try to improve this, but

    • The flat orbifold quotient of the 4-torus by the sign involution on all four canonical coordinates is the flat compact 4-dimensional orbifold known as the Kummer surface T 4⫽ℤ 2T^4 \sslash \mathbb{Z}_2

    suggests that’s there’s just one Kummer surface, but in fact there’s a whole moduli space of them, since different ways of making T 4T^4 into an abelian variety can make T 4⫽ℤ 2T^4 \sslash \mathbb{Z}_2 into non-isomorphic abelian varieties, all of which are called Kummer surfaces. There’s a cool paper about this:

    • CommentRowNumber8.
    • CommentAuthorUrs
    • CommentTimeMar 31st 2024
    • (edited Mar 31st 2024)

    after the word “4-torus” I have added in parenthesis “equipped with some complex structure”. Also added pointer to Taormina & Wendland’s §1.

    On the definition of CYs there is notoriously some ambiguity: sometimes (such as on the nnLab since revision 8) the condition H 1≤•≤n−1(X,𝒪 X)=0H^{1 \leq \bullet \leq n-1}(X, \mathcal{O}_X) = 0 is included (qualified in revision 18 by myself, it seems), which is probably why the entry used to be specific just a couple of words “later”.

    diff, v40, current

1 to 8 of 8

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