Related papers: Sandwich theorems for Shioda-Inose structures

The purpose of this note is to prove that the symplectic mapping class groups of many K3 surfaces are infinitely generated. Our proof makes no use of any Floer-theoretic machinery but instead follows the approach of Kronheimer and uses…

In this paper, we introduce multi-layer quiver and show how to construct an $(n+1)$-slice algebras of infinite type from an $n$-slice algebra of infinite type using the bound quivers. This leads to constructing $(n+1)$-slice algebras of…

In this article we will show that there are infinitely many symmetric, integral 3 x 3 matrices, with zeros on the diagonal, whose eigenvalues are all integral. We will do this by proving that the rational points on a certain non-Kummer,…

The aim of this paper is to generalize results known for the symplectic involutions on K3 surfaces to the order 3 symplectic automorphisms on K3 surfaces. In particular, we will explicitly describe the action induced on the lattice…

We show that double cosets of the infinite symmetric group with respect to some special subgroups admit natural structures of semigroups. We interpret elements of such semigroups in combinatorial terms (chips, colored graphs,…

For each member of an infinite family of homology classes in the K3-surface E(2), we construct infinitely many non-isotopic symplectic tori representing this homology class. This family has an infinite subset of primitive classes. We also…

We shall characterize the Fermat K3 surface, among all complex K3 surfaces, by means of its finite group symmetries.

By a lattice theoretic approach, Brandhorst--Hashimoto has made the list of K3 surfaces with finite groups of automorphisms which properly contain a maximal symplectic automorphism group. We give $3$ different explicit descriptions to the…

Shimura curves are moduli spaces of abelian surfaces with quaternion multiplication. Models of Shimura curves are very important in number theory. Klein's icosahedral invariants $\mathfrak{A},\mathfrak{B}$ and $\mathfrak{C}$ give the…

Using a quartic surface and its rational curves we can give an infinite number of integer hexahedra; these are 6 sided 3d solids, each face a trapezoid, with all sides and diagonals having intger lengths.

Let S be a K3 surface obtained as triple cover of a quadric branched along a genus 4 curve. Using the relation with cubic fourfolds, we show that S has finite dimensional motive, in the sense of Kimura. We also establish the Kuga-Satake…

We show that the classical Kuga-Satake construction gives rise, away from characteristic 2, to an open immersion from the moduli of primitively polarized K3 surfaces (of any fixed degree) to a certain regular integral model for a Shimura…

We consider a product of three copies of infinite symmetric group and its representations spherical with respect to the diagonal subgroup. We show that such representations generate functors from a certain category of simplicial…

The classical Kummer construction attaches to an abelian surface a K3 surface. As Shioda and Katsura showed, this construction breaks down for supersingular abelian surfaces in characteristic two. Replacing supersingular abelian surfaces by…

We prove that the moduli spaces of K3 surfaces with non-symplectic involutions are unirational. As a by-product we describe configuration spaces of 4<d<9 points in the projective plane as arithmetic quotients of type IV.

The Shafarevich conjecture for K3 surfaces asserts the finiteness of isomorphism classes of K3 surfaces over a fixed number field admitting good reduction away from a fixed finite set of finite places. Andr\'{e} proved this conjecture for…

In a recent paper Ahlgren, Ono and Penniston described the L-series of K3 surfaces from a certain one parameter family in terms of those of a particular family of elliptic curves. The Tate conjecture predicts the existence of a…

This is a latest survey article on embeddings of multibranched surfaces into 3-manifolds.

A classical question in geometry is whether surfaces with given geometric features can be realized as embedded surfaces in Euclidean space. In this paper, we construct an immersed, but not embedded, infinite $\{3,7\}$-surface in…

In this article, we study quasimaps to moduli spaces of sheaves on a $K3$ surface $S$. We construct a surjective cosection of the obstruction theory of moduli spaces of quasimaps. We then establish reduced wall-crossing formulas which…