All Questions
6
questions
6
votes
1
answer
901
views
Complex structures on a K3 surface as a hyperkähler manifold
A hyperkähler manifold is a Riemannian manifold of real dimension $4k$ and holonomy group contained in $Sp(k)$. It is known that every hyperkähler manifold has a $2$-sphere $S^{2}$ of complex ...
- 375
6
votes
0
answers
850
views
Possible automorphism groups of a K3 surface
Which finite groups are automorphism groups of polarized K3 surfaces (let's say over ℂ)?
...and does the answer change is I remove "polarized"?
(polarized = equipped with an ample line bundle)
- 42.2k
5
votes
2
answers
522
views
density of singular K3 surfaces
By singular K3 I mean a smooth complex K3 with Néron-Severi rank equal to 20.
Are singular K3 surfaces dense in the moduli space of polarized K3 surfaces?
- 3,697
5
votes
1
answer
683
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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
135
views
Moduli space with exceptional Mukai vector and tangent spaces at strictly semistable bundles
Assume we work (over $\mathbb{C}$) on a polarized K3 surface $(X,L)$ with a line bundle $M$ on $X$ such that $M^2=-6$ and $ML=0$ as well as $h^0(M)=h^2(M)=0$ and thus $h^1(M)=1$.
Then $E=\mathcal{O}_X\...
- 1,015
1
vote
2
answers
459
views
Isotrivial K3 family and Picard number
Is it true that any family of K3 surfaces over $\mathbb{C}$ whose Picard number is constant is isotrivial? Here isotrivial means locally analytically trivial.
Speculation: Let $\mathcal{M}$ be the ...
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