Related papers: On rational varieties of small degree

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…

The parametric degree of a rational surface is the degree of the polynomials in the smallest possible proper parametrization. An example shows that the parametric degree is not a geometric but an arithmetic concept, in the sense that it…

We correct a misattribution in our book.

Let $X\subset P^n$ be a complex projective manifold of degree $d$ and arbitrary dimension. The main result of this paper gives a classification of such manifolds (assumed moreover to be connected, non-degenerate and linearly normal) in case…

We provide a sufficient condition for a polynomial ring, not necessarily commutative, to have a first-order definition for the rational integers.

We give a new short proof of the classification of rank at least two invariant subvarieties in genus three, which is due to Aulicino, Nguyen, and Wright. The proof uses techniques developed in recent work of Apisa and Wright.

We describe those unipotent representations of a finite group of Lie type which are defined over the rational numbers.

We investigate degree bounds for fields of rational invariants of representations of finite groups. We prove many cases of a bound for $\mathbb{Z}/p\mathbb{Z}$ conjectured by Blum-Smith, Garcia, Hidalgo, and Rodriguez. For arbitrary groups,…

We study the expressive power of the two-variable fragment of order-invariant first-order logic. This logic departs from first-order logic in two ways: first, formulas are only allowed to quantify over two variables. Second, formulas can…

In this work we provide effective bounds and classification results for rational $\QQ$-factorial Fano varieties with a complexity-one torus action and Picard number one depending on the invariants dimension and Picard index. This…

We introduce an invariant of varieties in positive characteristic which generalizes the a-number of an abelian variety. We calculate it in some examples and discuss its meaning for moduli.

This text is devoted to the theory of varieties, which provides an important tool, based in universal algebra, for the classification of regular languages. In the introductory section, we present a number of examples that illustrate and…

Introducing the notion of a rational system of measure preserving transformations and proving a recurrence result for such systems, we give sufficient conditions in order a subset of rational numbers to contain arbitrary long arithmetic…

The problem we consider is to define families of n-dimensional integrals, endowed with group actions as in Rhin-Viola's work on irrationality measures of $\zeta(2)$ and $\zeta(3)$, the values of which are linear forms, over the rationals,…

In program semantics and verification, reasoning about loops is complicated by the need to produce two separate mathematical arguments: an invariant, for functional properties (ignoring termination); and a variant, for termination (ignoring…

We prove inversion of adjunction for higher rational singularities.

We introduce six new algebraic invariants for rational difference equations. We use these invariants to perform a reduction of order in each case. This reduction of order allows us to find forbidden sets in each case. These six cases…

In computer science, various logical languages are defined to analyze properties of systems. One way to pinpoint the essential differences between those logics is to compare their expressivity in terms of distinguishing power and expressive…

This paper is a sequel to [8] where we introduced an invariant, called canonical degree, of Cohen-Macaulay local rings that admit a canonical ideal. Here to each such ring with a canonical ideal, we attach a different invariant, called…

Rational pairs generalize the notion of rational singularities to reduced pairs $(X,D)$. In this paper we deal with the problem of determining whether a normal variety $X$ has a rationalizing divisor, i.e. a reduced divisor $D$ such that…