Related papers: Smooth double covers of K3 surfaces

We study Fourier-Mukai equivalence of K3 surfaces in positive characteristic and show that the classical results over the complex numbers all generalize. The key result is a positive-characteristic version of the Torelli theorem that uses…

Motivated by gauge theory on manifolds with exceptional holonomy, we construct examples of stable bundles on K3 surfaces that are invariant under two involutions: one is holomorphic; and the other is anti-holomorphic. These bundles are…

Inspired by the ideas of the minimal model program, Shepherd-Barron, Koll\'ar, and Alexeev have constructed a geometric compactification for the moduli space of surfaces of log general type. In this paper, we discuss one of the simplest…

We consider algebraic manifolds $Y$ of dimension 3 over $\Bbb{C}$ with $H^i(Y, \Omega^j_Y)=0$ for all $j\geq 0$ and $i>0$. Let $X$ be a smooth completion of $Y$ with $D=X-Y$, an effective divisor on $X$ with normal crossings. If the…

We prove that any hyper-K\"{a}hler sixfold $K$ of generalized Kummer type has a naturally associated manifold $Y_K$ of $\mathrm{K}3^{[3]}$-type. It is obtained as crepant resolution of the quotient of $K$ by a group of symplectic…

We study a family of lattice polarized $K3$ surfaces which is an extension of the family of Kummer surfaces derived from principally polarized Abelian surfaces. Our family has two special properties. First, it is coming from a resolution of…

We prove that the moduli spaces of K3 surfaces with non-symplectic involution are rational for four deformation types. With the previous results, this establishes the rationality of those moduli spaces except two classical cases.

Let $S \subset \mathbb{P}^g$ be a smooth $K3$ surface of degree $2g-2$, $g \geq 3$. We classify all the cases for which $h^0(\mathcal{N}_{S/\mathbb{P}^g}(-2)) \neq 0$ and the cases for which $h^0(\mathcal{N}_{S/\mathbb{P}^g}(-2)) <…

We give a list of possibilities for surfaces of general type with $p_g=0$ having an involution $i$ such that the bicanonical map of $S$ is not composed with $i$ and $S/i$ is not rational. Some examples with $K^2=4,...,7$ are constructed as…

We give necessary and sufficient conditions for a big and nef line bundle L of any degree on a K3 surface or Enriques surface to be k-very ample and k-spanned. Furthermore, we give necessary and sufficient conditions for a spanned and big…

We show several examples of integrable systems related to special K3 and rational surfaces (e.g., an elliptic K3 surface, a K3 surface given by a double covering of the projective plane, a rational elliptic surface, etc.). The construction,…

We prove the automorphic property of the invariant of K3 surfaces with involution, which we obtained using equivariant analytic torsion, in the case where the dimension of the moduli space is less than or equal to 2.

We consider the geometry of a general polarized K3 surface $(S,h)$ of genus 16 and its Fourier-Mukai partner $(S',h')$. We prove that $S^{[2]}$ is isomorphic to the moduli space $M_{S'}(2,h',7)$ of stable sheaves with Mukai vector…

Kodaira fibred surfaces are a remarkable example of projective classifying spaces, and there are still many intriguing open questions concerning them, especially the slope question. The topological characterization of Kodaira fibrations is…

We discuss N=2 supersymmetric compactifications to four dimensions from the point of view of F-theory and heterotic theory. In a relatively simple setup, we illustrate the spectral theory for vector bundles on K3xT^2 and discuss the…

Every Fourier--Mukai equivalence between the derived categories of two K3 surfaces induces a Hodge isometry of their cohomologies viewed as Hodge structures of weight two endowed with the Mukai pairing. We prove that this Hodge isometry…

We prove that every K3 surface with automorphism group $(\mathbb{Z}/2\mathbb{Z})^2$ admits an explicit birational model as a double sextic surface. This model is canonical for Picard number greater than 10. For Picard number greater than 9,…

Using the Kodaira dimension and the fundamental group of X, we succeed in classifying algebraic surfaces which are dominable by C^2 except for certain cases in which X is an algebraic surface of Kodaira dimension zero and the case when X is…

We give an existence result on (H,A)-stable sheaves on a K3 or abelian surface X with primitive triple of invariants (rank,first Chern class,Euler characteristics) in the integral cohomology lattice. Such a result yields the existence of…

We show that a Hilbert scheme of conics on a Fano fourfold double cover of $\mathbb{P}^2\times\mathbb{P}^2$ ramified along a divisor of bidegree $(2,2)$ admits a $\mathbb{P}^1$-fibration with base being a hyper-K\"{a}hler fourfold. We…