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Let $X$ be a smooth projective threefold with $h^{0,1}(X) = h^{0,2}(X)=0$ that has a smooth anticanonical section $D$. Then $D$ is necessarily a $K3$ surface. Consider a subgroup $$Pic_X(D) = i^*(Pic …

Recall that a $K3$ surface is called exceptional if its Picard number is 20. The Fermat quartic $K3$ surface in $\mathbb P^3$ is exceptional. My question is, Are there infinitely many non-isomorphi …

$\DeclareMathOperator\Pic{Pic}$Let $X$ be a K3 surface (algebraic, complex). An involution $\sigma:X\rightarrow X$ is called non-symplectic if it acts as multiplication by $-1$ on $H^{2,0}(X)=\Bbb{C}\ …

Is there a $K3$ surface (algebraic, complex) that has infinitely many automorphisms of finite order? Many K3 surfaces have infinite automorphism groups. In particular, all K3 surfaces of Picard ra …

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 …

Consider a smooth projective threefold $\overline W$, constructed in section 4 of this paper. This threefold is a resolution of singularities of the quotient of a product of a K3 surface and $\mathbb …

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 ${\r …

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 …

I am considering a certain $K3$ surface that is lattice-polarized in two ways. This leads to the following simple problem in lattice theory: (Let me borrow notations for lattice from Ch.14 of this boo …