All Questions
6
questions
5
votes
1
answer
433
views
Spherical objects on Kummer surfaces
Spherical objects $E$ in the derived category of coherent sheaves over a K3 surface satisfy:
$\operatorname{Hom}(E,E)=\mathbb{C}$,
$\operatorname{Ext}^2(E,E)=\mathbb{C}$,
$\operatorname{Ext}^i(E,E)=0$...
- 51
5
votes
2
answers
918
views
Singular K3 -- mathematical meaning?
There's a very interesting text by Cumrun Vafa called Geometric Physics.
Here I'm particularly interested in Chapter 4, where we take a Calabi-Yau manifold presented as a degenerating fibration:
...
- 14.8k
2
votes
0
answers
191
views
2 K3s and cubic fourfolds containing a plane
Two K3 surfaces show up when talking about cubic fourfolds containing a plane. Let $P\subset X\subset \mathbb{P}^5$ be the plane inside the cubic. Since $P$ is cut out by 3 linear equations then $X$ ...
- 3,697
2
votes
0
answers
100
views
Could we construct an inverse transform for the equivalence $D^b(X)\to D^b(M)$ between a K3 surface and its moduli space of semistable sheaves?
Let $X$ be a K3 surface and fix an ample line bundle on $X$. Let $v\in \widetilde{H}(X,\mathbb{Z})$ be a Mukai vector and $M(v)$ be the moduli space of semi-stable coherent sheaves on $X$ with Mukai ...
- 8,637
2
votes
0
answers
884
views
Cubic fourfold and K3 surface: geometric constructions of Hodge isometry
Hodge structure on K3 surface (the middle line of Hodge diamond is 1 20 1) is similar to the Hodge structure of cubic fourfold (the middle line of Hodge diamond of primitive cohomology is 0 1 20 1 0). ...
- 600
1
vote
0
answers
111
views
Does the Mukai's lemma hold for non-algebraic $K3$ surfaces?
In Huybrechts' book Fourier-Mukai Transforms in Algebraic Geometry I found the following result due to Mukai (Page 232, Lemma 10.6)
Let $X$ and $Y$ be two $K3$ surfaces. Then the Mukai vector of any ...
- 8,637