All Questions
Tagged with k3-surfaces reference-request
14
questions
33
votes
1
answer
1k
views
$\int_0^\infty x \, [J_0(x)]^5 \, dx$: source and context, if any?
QUESTION
Numerical calculation with gp (first to the default 38-digit
precision, then tripled) supports the conjecture that
$$
\int_0^\infty x \, [J_0(x)]^5 \, dx =
\frac{\Gamma(1/15) \, \Gamma(2/15) ...
- 76.8k
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
8
votes
0
answers
244
views
Fundamental group of moduli space of K3's
According to Rizov (https://arxiv.org/abs/math/0506120), the moduli stack of primitively polarized K3 surfaces of degree 2d $\mathcal{M}_{d}$ is a Deligne-Mumford stack over $\mathbb{Z}$. I'm looking ...
- 111
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
3
votes
0
answers
91
views
Are supersingular K3 surfaces unirational?
There is a conjecture due to Artin, Rudakov, Shafarevich, Shioda that supersingular K3 surfaces over a finite field are unirational. This paper claims to prove this result but it has had a recent ...
- 7,498
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
96
views
Amoeba for a K3 surface in $\mathbb {CP}^3$
Let $X=X_\Delta$ be the toric variety associated to a reflexive polyhedron $\Delta$.
Consider a Calabi-Yau hypersurface $Y\subset X$, and the image of $Y$ under the moment map $\mu:X\to \Delta$ has ...
- 2,709
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
1
answer
174
views
Characterization of $d$-gonal curves on a K3 surface
Let $X$ be a K3 surface and $C$ a curve on $X$. We say that $C$ is $d$-gonal if it admits a pencil of degree $d$ (and none of smaller degree).
I am wondering if there exist characterizations of $d$-...
- 761