Related papers: Construction of Brauer-Severi Varieties

The generators of the group of birational automorphisms of any Severi-Brauer surface non-isomorphic over an algebraically non-closed field to the projective plane are explicitly described.

We study the evaluation maps given by elements of the Brauer group of varieties over local fields. We show constancy of the aforementioned maps in several interesting cases.

We compute the Brauer group of the moduli stack of hyperelliptic curves $\mathcal{H}_g$ over any field of characteristic zero. In positive characteristic, we compute the part of the Brauer group whose order is prime to the characteristic of…

We determine the decomposition matrices of the Brauer algebra over the complex field.

We compute the dimensions of all the secant varieties to the tangential varieties of all Segre-Veronese surfaces. We exploit the typical approach of computing the Hilbert function of special 0-dimensional schemes on projective plane by…

We give algorithms to compute isomorphism classes of ordinary abelian varieties defined over a finite field $\mathbb{F}_q$ whose characteristic polynomial (of Frobenius) is square-free and of abelian varieties defined over the prime field…

We analyse infinitesimal deformations of morphisms of locally free sheaves on a smooth projective variety $X$ over an algebraically closed field of characteristic zero. In particular, we describe a differential graded Lie algebra…

We prove an equivariant Riemann-Roch formula for divisors on algebraic curves over perfect fields. By reduction to the known case of curves over algebraically closed fields, we first show a preliminary formula with coefficients in Q. We…

Let X be a smooth projective rational variety carrying a regular action of a finite abelian group G. We give examples of effective computation of the Brauer group of the quotient stack [X/G] in dimensions 2 and 3 using residues in Galois…

We consider the problem of counting the number of varieties in a family over a number field which contain a rational point. In particular, for products of Brauer-Severi varieties and closely related counting functions associated to Brauer…

We determine the blocks of the periplectic Brauer algebra over any field of odd characteristic.

Let $k$ be a field that is finitely generated over the field of rational numbers and $Br(k)$ the Brauer group of $k$. Let $X$ be an absolutely irreducible smooth projective variety over $k$, let $Br(X)$ be the cohomological…

In this paper we present an algorithm for computing all algebraic intermediate subfields in a separably generated unirational field extension (which in particular includes the zero characteristic case). One of the main tools is Groebner…

We determine the blocks of the Brauer algebra in characteristic zero. We also give information on the submodule structure of standard modules for this algebra.

We introduce four invariants of algebraic varieties over imperfect fields, each of which measures either geometric non-normality or geometric non-reducedness. The first objective of this article is to establish fundamental properties of…

We show that for two afii varieties over an arbitrary field of characteristic zero, there is no general form of an algorithm for checking the presence of an embedding of one algebraic variety in another. Moreover, we establish this for…

This paper deals with properties of the algebraic variety defined as the set of zeros of a "deficient" sequence of multivariate polynomials. We consider two types of varieties: ideal-theoretic complete intersections and absolutely…

We develop a theory of sesquilinear forms over finite fields, investigating their representations via polynomials and coefficient matrices, along with classification results for these forms. Through their connection to quadratic forms, we…

We develop a probabilistic algorithm of Kronecker type for computing a Kronecker representation of a zero-dimensional linear section of an algebraic variety $V$ defined over a perfect field $k$. The variety $V$ is the Zariski closure of the…

We provide a general algorithm for the computation of the unramified Brauer group of quotients of rational varieties by finite groups.