All Questions
9
questions
19
votes
1
answer
747
views
Vector field on a K3 surface with 24 zeroes
In https://mathoverflow.net/a/44885/4177, Tilman points out that one can use a $K3$ surface minus the zeroes of a generic vector field to build a nullcobordism for $24[SU(2)]$. Given that a) this is a ...
- 33.2k
8
votes
0
answers
336
views
Concrete example of $K3$ surfaces with Picard number 18 and does not admit Shioda-Inose structure?
I am looking for some explicit examples of (elliptic) $K3$-families defined over a number field (better to be over $\mathbb{Q}$) with Picard number $18$ but does not admit Shioda-Inose structure, i.e. ...
- 451
5
votes
1
answer
799
views
Reference request: Generic k3 surface has Picard number 1
I keep running into the statement that "the generic k3 surface has Picard rank 1".
For instance the answer of this question (end) and this paper (following Example 1.1) or this paper (proof ...
- 101
5
votes
2
answers
449
views
Reference for Automorphisms of K3 surfaces
I am looking for some introductory reference concerning Automorphisms (of finite order) on K3 surfaces. Any suggestion?
- 761
5
votes
1
answer
707
views
Training towards research on k3 surfaces
I am a graduate student learning basic algebraic geometry (from Hartshorne, Shafarevich). I'm planning to work in k3 surfaces (arithmetic and geometric properties, in my guide's words). I came to know ...
5
votes
1
answer
683
views
On the cohomology ring of the Hilbert scheme of points on k3 or abelian surfaces
There are many results on the cohomology of the Hilbert scheme of points of a surface.
Gottsche calcaluted the Betti numbers and Nakajima got the generators of the cohomology. Also
there are results ...
- 118
2
votes
1
answer
257
views
Very general quartic hypersurface in $\mathbb{P}^3$ has Picard group $\mathbb{Z}$
I am looking for a reference from which I can cite the following statement:
The Picard group of a very general quartic hypersurface $X\subset\mathbb{P}^3$ is generated by the class of a hyperplane ...
- 2,863
2
votes
1
answer
117
views
Fixed locus in the linear system associated to the ramification locus of a K3 double cover of a Del Pezzo surface
Let $X$ be a (smooth) del Pezzo surface over $\mathbb{C}$. Let $\Delta_0$ be a (smooth irreducible) generic curve in the linear system $|-2K_X|$. Let $\rho : S \rightarrow X$ be the double cover of $X$...
- 7,100
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