# Tagged Questions

**3**

votes

**1**answer

141 views

### Spectral sequence associated to elliptic fibration degenerates?

Let $\phi:S\rightarrow \mathbb{CP}^1$ be an elliptic fibration of a K3 surface. When is the Leray spectral sequence associated to the fibration $E_2$-degenerate? Are there any good criteria for the ...

**3**

votes

**1**answer

188 views

### K3 surface with $D_{14}$ singular fiber

Let $X$ be an elliptic K3 surface with $D_{14}$ singular fiber. Do you know an explicit equation for such $X$? Also, how many disjoint sections such fibration admits? Any reference would be greatly ...

**3**

votes

**0**answers

136 views

### Topology of K3 as a sum of two abelian fibrations.

Let $E$ be a blow-up of $\mathbb{P}^2$ at 9-points in the bases locus of a pencil of elliptic curves (A $T^2$ fibration over $S^2$).
K3 surfaces is obtained by removing a fiber from two copies of $E$ ...

**2**

votes

**0**answers

253 views

### Singular fibers of an elliptic fibered K3 surface.

Let $f:S\rightarrow \mathbb{P}^1$ be an elliptic K3 surface. Assume that $\mathrm{Pic}(S)\cong U$, where $U$ stands for the hyperbolic lattice. I think that the elliptic fibration has only singular ...

**7**

votes

**1**answer

474 views

### Dodecahedral K3?

In pondering
this
MO question and in particularly its 1st answer, and answers to
this one recently posed, I realized there ought to be a dodecahedral K3 surface $X$.
This $X$ would fiber as an ...

**10**

votes

**3**answers

731 views

### A K3 over $P^1$ with six singular $A_1$- fibers?

Hirzebruch, in the paper 'Arrangements of Lines and Algebraic Surfaces'
constructs a special $K3$ surface out of a 'complete quadrilateral' in
$CP^2$. A complete quadritlateral consists of
4 ...