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 $n$Lab since revision 8) the condition $H^{1 \leq \bullet \leq n-1}(X, \mathcal{O}_X) = 0$ 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”.

]]>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$T^4 \sslash \mathbb{Z}_2$

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 $T^4$ into an abelian variety can make $T^4 \sslash \mathbb{Z}_2$ into non-isomorphic abelian varieties, all of which are called Kummer surfaces. There’s a cool paper about this:

]]>The first sentence of the article defined a K3 surface to be a Calabi-Yau variety of dimension $2$, which was wrong: we also need the condition $H^1(X, \mathcal{O}_X)=0$, which appeared later. I fixed it.

]]>added statement of SU-bordism class (here)

]]>added pointer to today’s

- Shamit Kachru, Arnav Tripathy, Max Zimet,
*K3 metrics*(arXiv:2006.02435)

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

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

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