# Tagged Questions

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### Linear system on an abelian surface

On a K3 surface $S$, a linear system $|C|$ is said to be hyperelliptic if the corresponding map is of degree 2 and the image is of degree $g_a(C)-1$ in $\mathbb P^{g_a}$. For $g_a(C) > 2$, if ...
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### Does $h^1(D)=0$ imply numerical connectedness on K3 surfaces?

Let $X$ be a complex K3 surface and $D$ an effective divisor on $X$. We shall say: $D$ is connected if its support is connected. $D$ is numerically connected if for any non-trivial effective ...
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### 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 ...
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### Weyl group of a K3 surface

I am wondering wether the action of the Weyl group $W_X$ of a K3 surface $X$ is transitive on the sets of curves of fixed genus. Suppose $W_X$ is non-trivial. Given two curves $C,C'$ of genus ...
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### Reference for Automorphisms of K3 surfaces

I am looking for some introductory reference concerning Automorphisms (of finite order) on K3 surfaces. Any suggestion?
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### A question on an elliptic fibration of the Enriques surface

Let $S$ be an Enriques surface over complex numbers. It is known that $S$ admits an elliptic fibration over $\mathbb{P}^1$ with $12$ nodal singular fibers and $2$ double fibers. How can I see this ...
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### octic K3s inside cubic 4-folds

From the Thesis of B.Hassett I seem to understand that a smooth cubic 4-fold $X$ containing a $\mathbb{P}^2$ should contain also a octic K3, but I cannot see a natural way by which this K3 octic could ...
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### K3 surfaces with good reduction away from finitely many places

Let S be a finite set of primes in Q. What, if anything, do we know about K3 surfaces over Q with good reduction away from S? (To be more precise, I suppose I mean schemes over Spec Z[1/S] whose ...