All Questions
Tagged with k3-surfaces dg.differential-geometry
8
questions
8
votes
2
answers
452
views
Necessary condition on Calabi-Yau manfiold to be a hypersurface in a Fano manifold
Let $X$ be a smooth projective Calabi-Yau threefold. Are there any known obstructions to it
being a member of a base-point-free linear system in a nef-Fano fourfold?
What, in anything, is known ...
- 5,156
7
votes
0
answers
204
views
Does there exists a compact Ricci-flat K3 surface whose metric tensor is expressed in explicit formula?
Yau's theorem showed the existence. But I had difficulty finding examples other than complex tori. Any information will be appreciated.
- 193
6
votes
0
answers
347
views
Quantifying the failure of geometric formality in K3 surfaces
It is known that K3 surfaces are never geometrically formal [1]. That is, the wedge product of two harmonic forms on an arbitrary K3 surface is in general not harmonic, or equivalently, the space $\...
- 271
5
votes
2
answers
940
views
Are any two K3 surfaces over C diffeomorphic?
Let $S$ be a K3 surface over $\mathbb{C}$, that is, $S$ is a simply connected compact smooth complex surface whose canonical bundle is trivial. I recall reading somewhere that any two such surfaces ...
- 20.6k
4
votes
2
answers
312
views
Algebraic cycles on a K3 surface after hyperKahler rotation.
I would like to find a gap in the following observation. I found a suspicious part but cannot prove it wrong. I would appreciate your assistance.
Let $M$ be a lattice of signature $(1,t)$ and $S$ be ...
- 41
2
votes
1
answer
168
views
Concrete descriptions of $S^1$-bundles over smooth manifold $Y$ underying a K3 surface
Let $Y$ be the smooth manifold underlying a K3 surface. As a manifold, $Y$ is diffeomorphic to $\{[x_0:x_1:x_2:x_3]\in\mathbb{C}P^3\colon X_0^4+x_1^4+X_2^4+X_3^4=1\}$. It is well known that $H^2(Y,\...
- 133
2
votes
1
answer
460
views
Isometry of K3 surface.
Let $S$ be a K3 surface and $\iota$ be anti-symplectic involution of $S$. Suppose that $g$ is a Kahler-Einstein metric on $S$. My question is;
Why $\iota$ is an isometry of $S$ with respect to $g$?...
- 21
2
votes
0
answers
83
views
Explicit Lagrangian fibrations of a K3 surface
I would like to look at the behaviour of the fibres of a Lagrangian fibration (such that at least some fibres are not special Lagrangian) $X\to\mathbb{CP}^1$ under the mean curvature flow (in relation ...
- 355