Related papers: Construction of Brauer-Severi Varieties

In 2013, Abo and Wan studied the analogue of Waring's problem for systems of skew-symmetric forms and identified several defective systems. Of particular interest is when a certain secant variety of a Segre-Grassmann variety is expected to…

We study the relationship between the equations defining a projective variety and properties of its secant varieties. In particular, we use information about the syzygies among the defining equations to derive smoothness and normality…

We classify finite groups that can act by automorphisms and birational automorphisms on non-trivial Severi-Brauer surfaces over fields of characteristic zero.

We present an explicit algorithmic method for computing square roots in quaternion algebras over global fields of characteristic different from 2.

It is conjectured that the Brauer--Manin obstruction is expected to control the existence of 0-cycles of degree 1 on smooth proper varieties over number fields. In this paper, we prove that the existence of Brauer--Manin obstruction to…

We propose several techniques to construct complete permutation polynomials of finite fields by virtue of complete permutations of subfields. In some special cases, any complete permutation polynomials over a finite field can be used to…

We classify products of symmetric powers of a Severi-Brauer variety, up-to stable birational equivalence. The description also includes Grassmannians and moduli spaces of genus 0 stable maps.

We compute the number of points over finite fields of some algebraic varieties related to cluster algebras of finite type. More precisely, these varieties are the fibers of the projection map from the cluster variety to the affine space of…

Given $p$ polynomials of $n$ variables over a field $k$ of characteristic 0 and a point $a \in k^n$, we propose an algorithm computing the local Bernstein-Sato ideal at $a$. Moreover with the same algorithm we compute a constructible…

In the current paper we prove that any Severi variety on a Hirzebruch surface contains a unique component parameterizing irreducible nodal curves of the given genus in characteristic zero.

We study completeness in partial differential varieties. We generalize many results from ordinary differential fields to the partial differential setting. In particular, we establish a valuative criterion for differential completeness and…

The purpose of this paper is to show how Rees algebras can be applied in the study of singularities embedded in smooth schemes over perfect fields. In particular, we will study situations in which the multiplicity of a hypersurface is a…

Using the classical S.Lie method we obtain a complete description of infinitesimal symmetries of a holomorphic PDE system defining the Segre family of a real analytic hypersurface. This gives a new proof of some well known results of CR…

We present a class of toric varieties $V$ which, over any algebraically closed field of characteristic zero, are defined by codim $V$+1 binomial equations.

We investigate the birational section conjecture for curves over function fields of characteristic zero and prove that the conjecture holds over finitely generated fields over Q if it holds over number fields.

We propose a conceptual framework that leads to an abstract characterization for the exact solvability of Calabi-Yau varieties in terms of abelian varieties with complex multiplication. The abelian manifolds are derived from the cohomology…

We consider those projective bundles (or Brauer-Severi varieties) over an abelian variety that are homogeneous, i.e., invariant under translation. We describe the structure of these bundles in terms of projective representations of…

We discuss logical links among uniformity conjectures concerning K3 surfaces and abelian varieties of bounded dimension defined over number fields of bounded degree. The conjectures concern the endomorphism algebra of an abelian variety,…

We show how one can construct new autoequivalences of some Calabi-Yau and hyperk"ahler varieties by passing from a smooth projective surface to the associated Hilbert scheme of points.

We construct explicit equations of Cartwright-Steger and related surfaces.