Related papers: Sandwich theorems for Shioda-Inose structures
A periodic automorphism of a surface $\Sigma$ is said to be extendable over $S^3$ if it extends to a periodic automorphism of the pair $(S^3,\Sigma)$ for some possible embedding $\Sigma\to S^3$. We classify and construct all extendable…
One can embed arbitrarily many disjoint, non-parallel, non-boundary parallel, incompressible surfaces in any three manifold with at least one boundary component of genus two or greater [4]. This paper proves the contrasting, but not…
In this paper, we study structural properties of finite mutation type quivers. In particular, we obtain a characterization of finite mutation type quivers that are associated with triangulations of surfaces and give a new numerical…
In this note, we construct three new infinite families of surfaces of general type with canonical map of degree 2 onto a surface of general type. For one of these families the canonical system has base points.
We study Fano fourfolds of K3 type with a conic bundle structure. We construct direct geometrical links between these fourfolds and hyperK\"ahler varieties. As a result we describe families of nodal surfaces that can be seen as…
We generalize Mukai and Shafarevich's definitions of isogenies between K3 surfaces over $\mathbb{C}$ to an arbitrary perfect field and describe how to construct isogenous K3 surfaces over $\bar{\mathbb{F}}_p$ by prescribing linear algebraic…
We prove that certain Fano fourfolds of K3 type constructed by Fatighenti-Mongardi have a multiplicative Chow-K\"unneth decomposition. We present some consequences for the Chow ring of these fourfolds.
We prove a surface embedding theorem for 4-manifolds with good fundamental group in the presence of dual spheres, with no restriction on the normal bundles. The new obstruction is a Kervaire-Milnor invariant for surfaces and we give a…
We construct a compact example of 7- dimensional manifold endowed with a weakly integrable generalized G_2-structure with respect to a closed and non trivial 3-form. Moreover, we investigate which type of SU(3)-structures on a 6-dimensional…
The aim of this paper is to construct "special" isogenies between K3 surfaces, which are not Galois covers between K3 surfaces, but are obtained by composing cyclic Galois covers, induced by quotients by symplectic automorphisms. We…
Within the framework of Berwald-Moor Geometry in H_3, the paper studies the construction of additive poly-angles (bingles and tringles). It is shown that, considering additiveness in the large, there exist an infinity of such poly-angles.
A K3 surface over a number field has infinitely many rational points over a finite field extension. For K3 surfaces of degree 2, arising as double covers of $\mathbb{P}^2$ branched along a smooth sextic curve, we give a bound for the degree…
This paper relates skein spaces based on the Kauffman bracket and spin structures. A spin structure on an oriented 3-manifold provides an isomorphism between the skein space for parameter A and the skein space for parameter -A. There is an…
We introduce (co)homology theory for multiple group racks and construct cocycle invariants of compact oriented surfaces in the 3-sphere using their 2-cocycles, where a multiple group rack is a rack consisting of a disjoint union of groups.…
We construct a K3 surface over an algebraically closed field of characteristic 2 which contains two sets of 21 disjoint smooth rational curves such that each curve from one set intersects exactly 5 curves from the other set. This…
In this note we prove analogues of the main theorems of complex multiplication for abelian varieties for K3 surfaces. This is done by studying the field of definition of the period morphism for complex K3 surfaces. More precisely we relate…
Global constructions of quantization deformation and obstructions are discussed for an arbitrary complex analytic space in terms of adapted (analytic) Hochschild cohomology. For K3-surfaces an explicit global construction of a Poisson…
We introduce and study tame homeomorphisms of surfaces of infinite type. These are maps for which curves under iterations do not accumulate onto geodesic laminations with non-proper leaves, but rather just a union of possibly intersecting…
We introduce the semi-infinite category of sheaves on the affine Grassmannian, and construct a particular object in it, which we call the the semi-infinite intersection cohomology sheaf. We relate it to several other entities naturally…
We prove that the first order deformations of two smooth projective K3 surfaces are derived equivalent under a Fourier--Mukai transform if and only if there exists a special isometry of the total cohomology groups of the surfaces which…