Related papers: Linear systems of rational curves on rational surf…

We show the existence of metrically dense entire curves in rationally connected complex projective manifolds confirming for this case a conjecture according to which such entire curves on projective manifolds exist if and only if these are…

A telegraphic survey of some of the standard results and conjectures about the set $C({\bf Q})$ of rational points on a smooth projective absolutely connected curve $C$ over ${\bf Q}$.

The sigma model on complex projective superspaces CP^{S-1|S} gives rise to a continuous family of interacting 2D conformal field theories which are parametrized by the curvature radius R and the theta angle \theta. Our main goal is to…

A rational triangle is a triangle with rational side lengths. We consider three different families of rational triangles having a fixed side and whose vertices are rational points in the plane. We display a one-to-one correspondence between…

In the open problem of classification of rational cuspidal plane curves it is essential to find good necessary conditions on the type of singularities of a curve C in order C to exit. Motivated by the study of the Seiberg-Witten invariant…

Let C be a projective Gorenstein curve over an algebraically closed field of characteristic 0. A generalized linear system on C is a pair (I,f) consisting of a torsion-free, rank-1 sheaf I on C and a map of vector spaces f to the space of…

By studying the theory of rational curves, we introduce a notion of rational simple connectedness for projective homogeneous spaces. As an application, we prove that over a function field of an algebraic surface, a projective homogeneous…

Let $C$ be a smooth plane curve of degree $d$ defined over an algebraically closed field $k$. A base point free complete very special linear system $g^r_n$ on $C$ is trivial if there exists an integer $m\ge 0$ and an effective divisor $E$…

Fix a smooth projetive curve $\mathcal {C}$ of genus $g\geq 2$ and a line bundle $\mathcal{L}$ on $\mathcal{C}$ of degree $d$. Let $M:= \mathcal{SU}_{\mathcal{C}}(r, \mathcal{L})$ be the moduli space of stable vector bundles on…

Let $C$ be an integral and projective curve whose canonical model $C'$ lies on a rational normal scroll $S$ of dimension $n$. We mainly study some properties on $C$, such as gonality and the kind of singularities, in the case where $n=2$…

This paper is concerned with projective rationally connected surfaces $X$ with canonical singularities and having non-zero pluri-forms, i.e. $(\Omega_X^1)^{[\otimes m]}$ has non-zero global sections for some m > 0, where…

There are no known failures of Bounded Negativity in characteristic 0. In the light of recent work showing the Bounded Negativity Conjecture fails in positive characteristics for rational surfaces, we propose new characteristic free…

We find a natural $L_{\omega_1,\omega}$-axiomatisation $\Sigma$ of a structure on the upper half-plane $\mathbb{H}$ as the covering space of modular curves. The main theorem states that $\Sigma$ has a unique model in every uncountable…

In [15], V. Jimenez and J. Llibre characterized, up to homeomorphism, the omega limit sets of analytic vector fields on the sphere and the projective plane. The authors also studied the same problem for open subsets of these surfaces.…

We give an effective iterative characterization of the classes of (smooth, rational) (-1)-curves on the blowup of the projective plane at general points. Such classes are characterized as having self-intersection -1, arithmetic genus 0, and…

It is argued that transformation processes (generation rules) showing evidence of a long evolutionary history in universal computing systems can be generalized. The explicit function class $ \Omega $ is defined as follows: "Operators whose…

We proved the existence of rational curves in every linear system on a general K3 surface and that all rational curves in the hyperplane class are nodal on a general K3 surface of small genus.

We study the rationality of some geometrically rational three-dimensional conic and quadric surface bundles, defined over the reals and more general real closed fields, for which the real locus is connected and the intermediate Jacobian…

For any Kahler surface which admits no nonzero holomorphic vectorfields, we consider the group of holomorphic automorphisms which induce identity on the second rational cohomology. Assuming the canonical linear system is without base points…

It is well known that an irreducible algebraic curve is rational (i.e. parametric) if and only if its genus is zero. In this paper, given a tolerance $\epsilon>0$ and an $\epsilon$-irreducible algebraic affine plane curve $\mathcal C$ of…