All Questions
Tagged with k3-surfaces at.algebraic-topology
3
questions
66
votes
1
answer
2k
views
Is there an octonionic analog of the K3 surface, with implications for stable homotopy groups of spheres?
The infamous K3 surface has many constructions in many fields ranging from algebraic geometry to algebraic topology. Its many properties are well known. For this question I am really interested in the ...
- 26.9k
5
votes
0
answers
113
views
Isotopy classes of $CP^1$ in 4-manifolds
Let $S_1$, $S_2$ be homologous embedded 2-spheres
in a compact smooth 4-manifold. Under which additional
conditions are they smoothly isotopic? I am interested
in the state of the art picture when $...
- 9,045
1
vote
1
answer
371
views
Understand the Mukai vector
Let $S$ be a K3 surface and $h:=c_1(i^*\mathcal{O}_{\mathbb{P^3}}(1))$, then we can compute that $c_1(S)=0,c_2(S)=6h^2$. Hence
\begin{align}
\sqrt{\text{td}(S)}=1+\frac{c_2(S)}{24}=1+\frac{1}{4}h^2
\...
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