Related papers: The G\"opel variety

The Plucker relations define a projective embedding of the Grassmann variety Gr(k,n). We give another finite set of quadratic equations which defines the same embedding, and whose elements all have rank 6. This is achieved by constructing a…

In this paper we prove the Geyer-Jarden conjecture on the torsion part of the Mordell-Weil group for a large class of abelian varieties defined over finitely generated fields of arbitrary characteristic. The class consists of all abelian…

Given a smooth genus three curve $C$, the moduli space of rank two stable vector bundles on C with trivial determinant embeds in $\mathbb{P}^8$ as a hypersurface whose singular locus is the Kummer threefold of $C$; this hypersurface is the…

In a remarkable article Ribet showed how to attach rational $2$-dimensional representations to elliptic ${\mathbb Q}$-curves. An abelian variety $A$ is a (weak) $K$-variety if it is isogenous to all of its $\text{Gal}_K$-conjugates. In this…

We prove that the stabiliser group G of the Segre variety product in PG(V) of three projective lines over a field F has four orbits on singular points of PG(V), and that G has five orbits on points of PG(V) if F is finite.

We prove that the mapping class group of a closed connected orientable surface of genus $g$ is generated by two elements of order $g$ for $g\geq 6$. Moreover, for $g\geq 7$ we found a generating set of two elements, of order $g$ and $g'$…

Let $X$ be a smooth complex projective algebraic variety. Let $\mathcal{G}$ be a $G$-banded gerbe with $G$ a finite abelian group. We prove an exact formula expressing genus $g$ orbifold Gromov-Witten invariants of $\mathcal{G}$ in terms of…

This paper deals with surfaces with many lines. It is well-known that a cubic contains 27 of them and that the maximal number for a quartic is 64. In higher degree the question remains open. Here we study classical and new constructions of…

Let $Z$ be a projective geometrically integral algebraic variety. This paper is concerned with estimating the number of rational points on $Z$ which have height at most $B$. The bounds obtained are uniform in varieties of fixed degree and…

A series of nonrepresentable relation algebras is constructed from groups. We use them to prove that there are continuum many subvarieties between the variety of representable relation algebras and the variety of coset relation algebras. We…

Let $G=P_6\Box P_6$ be the $6\times 6$ grid, the Cartesian product of two paths of six vertices. Let $T$ be the set of eight distinct vertices of $G$, called terminals, and assume that $T$ is partitioned into four terminal pairs…

Let X be an Abelian surface and C a holomorphic curve in X representing a primitive homology class. The space of genus g curves in the class of C is g dimensional. We count the number of such curves that pass through g generic points and we…

Let $N_{g}$ denote the closed non-orientable surface of genus $g$ and let ${\mathcal M} _g$ denote the mapping class group of $N_{g}$. Let ${\mathcal T} _g$ denote the twist subgroup of ${\mathcal M} _g$ which is the subgroup of ${\mathcal…

In this paper, we introduce new combinatorial invariants of any finite simple graph, which arise in toric topology. We compute the $i$-th (rational) Betti number and Euler characteristic of the real toric variety associated to a graph…

In this article we study the number of different cuboids $\mathcal{O}(N)$ that can be built with an arbitrary number $N$ of equal cubes. This problem is equivalent to find the number of different cuboids of volume $N$ with integer length…

We give a construction that provides infinitely many 2-connected, cubic, bipartite, and planar graphs G with 3k vertices and such that the number of disjoint copies of a 3-vertex path in G is less than k.

We study the L-series of cubic fourfolds. Our main result is that, if X/C is a special cubic fourfold associated to some polarized K3 surface $S$, defined over a number field K such that S^[2](K) is not empty, then X has a model over K such…

In this paper, we study the geometry of the moduli space of representations of the fundamental group of the complement of a torus link into an algebraic group G, an algebraic variety known as the G-character variety of the torus link. These…

Let G be a finite group and A a finite dimensional G-graded algebra over a field of characteristic zero. When A is simple as a G-graded algebra, by mean of Regev central polynomials we construct multialternating graded polynomials of…

The approach to p-adic wavelet theory from the point of view of representation theory is discussed. p-Adic wavelet frames can be constructed as orbits of some p-adic groups of transformations. These groups are automorphisms of the tree of…