Questions about K3 surfaces, which are smooth complex surfaces $X$ with trivial canonical bundle and vanishing $H^1(O_X)$. They are examples of Calabi-Yau varieties of dimension $2$.

learn more… | top users | synonyms

48
votes
1answer
941 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 ...
3
votes
1answer
1k views

Mirror symmetry for hyperkahler manifold

Hi there, I have some questions about the mirror symmetry of hyperkahler manifold and K3 surface. The well-known result said: the mirror symmetry for K3 surface is just given by its hyperkahler ...
7
votes
0answers
281 views

Mirror symmetry for polarized abelian surfaces and Shioda-Inose K3s

It is well known (cf. Dolgachev) that there is a beautiful notion of mirror symmetry for lattice-polarized K3 surfaces. That is, if we are given a rank $r$ lattice $M$ of signature $(1, r - 1)$ and a ...
1
vote
1answer
336 views

Picard group of a K3 surface generated by a curve

In Lazarsfeld's article "Brill Noether Petri without degenerations" he mentions the fact that for any integer $g \geq 2$, one may find a K3 surface $X$ and a curve $C$ of genus $g$ on $X$ such that ...
0
votes
2answers
208 views

K3 surface with a non-symplectic involution: a basic question

Let $X$ be a K3 surface (algebraic, complex). An involution $\sigma:X\rightarrow X$ is called non-symplectic if it acts trivially on $H^{2,0}(X)=\Bbb{C}\omega_X$ $\ $ (where $\omega_X$ is any nowhere ...