All Questions
5
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
3
votes
0
answers
247
views
K3 surfaces in Fano threefolds
By K3 surfaces and Fano threefolds, I mean smooth ones.
If a K3 surface $S$ is an anticanonical section of a Fano threefold $V$ of Picard rank one (hence, $Pic(V)=\mathbb Z H_V$ for some ample divisor ...
- 1,821
3
votes
0
answers
235
views
A K3 cover over a Del Pezzo surface
Let $V \rightarrow \mathbb P^2$ be the blow-up at two distinct points. ($V$ is a Del Pezzo surface of degree 7.)
Choose a smooth curve $C$ from the linear system $|-2K_V|$ and let $S \rightarrow V$ be ...
- 1,821
2
votes
0
answers
321
views
Stability notion to smoothing varieties under a flat deformation with a smooth total space
Is there any stability notion that led to an algebraic variety be smoothable in general for Fano varieties or for Calabi-Yau varieties?
Note that Friedman found a nesessary condition that $X$ to be ...
user21574
1
vote
1
answer
235
views
$K3$ surfaces in $\mathbb P^1 \times \mathbb P^1 \times \mathbb P^1$
I am considering $K3$ surfaces in $\mathbb P^1 \times \mathbb P^1 \times \mathbb P^1$ with an automorphism that preserves an ample divisor class.
For an automorphism $\rho$ of a $K3$ surface, let ${\...
- 1,821