Related papers: Construction of Symmetric Cubic Surfaces

We study equivariant birationality from the perspective of derived categories. We produce examples of nonlinearizable but stably linearizable actions of finite groups on smooth cubic fourfolds.

To a family of smooth projective cubic surfaces one can canonically associate a family of abelian fivefolds. In characteristic zero, we calculate the Hodge groups of the abelian varieties which arise in this way. In arbitrary characteristic…

Let $\Bbbk$ be a perfect field with algebraic closure $\overline{\Bbbk}$. If $H$ is a subgroup of plane automorphisms over $\Bbbk$ and $p\in\overline{\Bbbk}^2$ is a point, we describe the subgroup consisting of plane automorphisms which…

The paper is concerned with `geometrization' of smooth (i.e. with open stabilizers) representations of the automorphism group of universal domains, and with the properties of `geometric' representations of such groups. As an application, we…

This paper is about the family of smooth quartic surfaces $X \subset \mathbb{P}^3$ that are invariant under the Heisenberg group $H_{2,2}$. For a very general such surface $X$, we show that the Picard number of $X$ is 16 and determine its…

We produce a sequence of finite dimensional representations of the fundamental group $\pi_1(S)$ of a closed surface where all simple closed curves act with finite order, but where each non--simple closed curve eventually acts with infinite…

In this paper we classify non-symplectic automorphisms of order 8 on complex K3 surfaces in case that the fourth power of the automorphism has only rational curves in its fixed locus. We show that the fixed locus is the disjoint union of a…

In this paper we give for all $n \geq 2$, d>0, $g \geq 0$ necessary and sufficient conditions for the existence of a pair (X,C), where X is a K3 surface of degree 2n in $\matbf{P}^{n+1}$ and C is a smooth (reduced and irreducible) curve of…

In this paper, we highlight that the point group structure of elliptic curves over finite or infinite fields, may be also observed on singular cubics with a quadratic component. Starting from this, we are able to introduce in a very general…

K3-surfaces with antisymplectic involution and compatible symplectic actions of finite groups are considered. In this situation actions of large finite groups of symplectic transformations are shown to arise via double covers of Del Pezzo…

The sl_2-triples play a fundamental role for the structure theory of Lie algebras, and representation theory in general. Here we investigate sl_2-triples of global vector fields on schemes X in positive characteristics p>0, and develop a…

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

We first construct a real family of $SL(2,\mathbb{R})$-invariant symbol composition product $\{\sharp_\theta\}_{\theta\in,\mathbb{R}}$ on the analogue of the Schwartz space $S(\mathbb{D})$ on the hyperbolic plane…

Let $E$ be an elliptic curve over a quartic field $K$. By the Mordell-Weil theorem, $E(K)$ is a finitely generated group. We determine all the possibilities for the torsion group $E(K)_{tor}$ where $K$ ranges over all quartic fields $K$ and…

We explore the enumerative problem of finding lines on cubic surfaces defined by symmetric polynomials. We prove that the moduli space of symmetric cubic surfaces is an arithmetic quotient of the complex hyperbolic line, and determine…

We describe the Galois action on the middle $\ell$-adic cohomology of smooth, projective fourfolds $K_A(v)$ that occur as a fiber of the Albanese morphism on moduli spaces of sheaves on an abelian surface $A$ with Mukai vector $v$. We show…

Recently de Thanhoffer de V\"olcsey and Van den Bergh classified the Euler forms on a free abelian group of rank 4 having the properties of the Euler form of a smooth projective surface. There are two types of solutions: one corresponding…

In this paper, we evaluate the algebraic $K$-groups of a planar cuspidal curve over a perfect $\mathbb{F}_p$-algebra relative to the cusp point. A conditional calculation of these groups was given earlier by Hesselholt, assuming a…

Let $k$ be a field, and suppose that $\Gamma$ is a smooth $k$-group that acts on a connected, reductive $k$-group $\widetilde G$. Let $G$ denote the maximal smooth, connected subgroup of the group of $\Gamma$-fixed points in $\widetilde G$.…

Smooth cubic fourfolds are linked to K3 surfaces via their Hodge structures, due to work of Hassett, and via Kuznetsov's K3 category A. The relation between these two viewpoints has recently been elucidated by Addington and Thomas. In this…