Related papers: A virtually ample field that is not ample

We prove that every non-trivial valuation on an infinite superrosy field of positive characteristic has divisible value group and algebraically closed residue field. In fact, we prove the following more general result. Let $K$ be a field…

A slip on a paper concerning near-vector spaces is fixed. New characterization of near-vector spaces determined by finite fields is provided and the number (up to the isomorphism) of these spaces is exhibited.

We show that every non-trivial ordered abelian group $G$ is augmentable by infinite elements, i.e., we have $G\preccurlyeq H\oplus G$ for some non-trivial ordered abelian group $H$. As an application, we show that when $k$ is a field of…

It was shown in Part I that there exist strongly dense free subgroups in any semisimple algebraic group over a large enough field. These are nonabelian free subgroups all of whose subgroups are either cyclic or Zariski-dense. Here we show…

In this paper, we present a criterion for $(K,v)$ to be henselian and defectless in terms of finite complete sequences of key polynomials. For this, we use the theory of Mac Lane-Vaqui\'e chains and abstract key polynomials. We then prove…

We study k-jet ampleness of line bundles on hyperelliptic surfaces using vanishing theorems. Our main result states that on a hyperelliptic surface of an arbitrary type a line bundle of type (m,m) with m\geq k+2 is k-jet ample.

In this article, we introduce a new object, a virtual quadratic space, and its group of isometries. They are presented as natural generalizations of quadratic spaces and orthogonal groups. It is then shown that by replacing quadratic spaces…

We argue that the finiteness of quantum gravity amplitudes in fully compactified theories (at least in supersymmetric cases) leads to a bottom-up prediction for the existence of non-trivial dualities. In particular, finiteness requires the…

Recently, Corvaja and Zannier obtained an extension of the Subspace Theorem with arbitrary homogeneous polynomials of arbitrary degreee instead of linear forms. Their result states that the set of solutions in P^n(K) (K number field) of the…

Let $k$ be a field, $V$ be a $k$-vector space and $X\subset V$ an algebraic irreducible subvariety. We say that a function $f:X(k) \to k$ is weakly linear if its restriction to any two-dimensional linear subspace $W$ of $V$ contained in $X$…

Let X be a projective hypersurface in P_k^n of degree d <= n. In this paper we study the relation between the class [X] in K_0(Var_k) and the existence of k-rational points. Using elementary geometric methods we show, for some particular X,…

In Butler, J.Differential Geom. 39 (1):1--34,1994, the author gives a sufficient condition for a line bundle associated with a divisor D to be normally generated on $X=P(E)$ where E is a vector bundle over a smooth curve C. A line bundle…

Given a dominant rational self-map on a projective variety over a number field, we can define the arithmetic degree at a rational point. It is known that the arithmetic degree at any point is less than or equal to the first dynamical…

Let $K$ be a field whose absolute Galois group is finitely generated. If $K$ neither finite nor of characteristic 2, then every hyperelliptic curve over $K$ with all of its Weierstrass points defined over $K$ has infinitely many $K$-points.…

Non-smooth vector fields does not have necessarily the property of uniqueness of solution passing through a point and this is responsible to enrich the behavior of the system. Even on the plane non-smooth vector fields can be chaotic, a…

Given a real algebraic group $G$ acting on a linear space $V$, a vector $v\in V$ is called unstable if $0\in \overline{Gv}-Gv$, where the closure is taken with respect to the Zariski topology. A fundamental theorem of Kempf in geometric…

Let K be a number field and let A be its ring of integers. Let G be a connected, noncommutative, absolutely almost simple algebraic K-group. If the K-rank of G equals 2, then G(A[t]) is not finitely presented.

In this paper, we prove the ampleness conjecture and Serrano's conjecture for strictly nef divisors on K-trivial fourfolds. Specifically, we show that any strictly nef divisors on projective fourfolds with trivial canonical bundle and…

Regular groups and fields are common generalizations of minimal and quasi-minimal groups and fields, so the conjectures that minimal or quasi-minimal fields are algebraically closed have their common generalization to the conjecture that…

Let $k$ be a field of characteristic zero and $B$ a commutative integral domain that is also a finitely generated $k$-algebra. It is well known that if $k$ is algebraically closed and the "Field Makar-Limanov" invariant FML$(B)$ is equal to…