All Questions
3
questions
7
votes
1
answer
450
views
Do non-projective K3 surfaces have rational curves?
Define a compact Kähler surface $X$ to be a K3 surface if $X$ is simply connected, $K_X \simeq \mathcal{O}_X$, and $h^{0,1}=0$. If $X$ is projective, then a theorem typically attributed to Bogomolov ...
- 1,269
4
votes
1
answer
260
views
Kummer surfaces which are not projective
This is a question from an online note. Let $A$ be a two-dimensional $\mathbb C$-torus. And there is an involution on $A$: $A\to A, x\mapsto -x$. The action has 16 fixed points. Let $Y:=A/\{\pm1\}$, ...
- 343
3
votes
1
answer
353
views
(1/2) K3 surface or half-K3 surface: Ways to think about it?
I heard from string theorists thinking of the so-called "(1/2) K3 surface" or "half-K3 surface" as follows:
Let $T^2 \times S^1$ be a 3-torus with spin structure periodic in all directions. $T^2 \...
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