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added pointer to today’s
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:
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”.
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