Related papers: On a question of Sean Keel
We shall study moduli spaces of stable 1-dimensional sheaves on an elliptic ruled surface.
The conchoid of a surface $F$ with respect to given fixed point $O$ is roughly speaking the surface obtained by increasing the radius function with respect to $O$ by a constant. This paper studies {\it conchoid surfaces of spheres} and…
In this note we prove the semiampleness conjecture for klt Calabi--Yau surface pairs over an excellent base ring. As applications we deduce that generalised abundance and Serrano's conjecture hold for surfaces. Finally, we study the…
It is shown that the question raised in Section 5.7 of [1] has an affirmative answer.
The purpose of this note is to give a short, selfcontained proof of the following result: A complex surface which is diffeomeorphic to a rational surface is rational.
We show that ruled real hypersurfaces with constant mean curvature in the complex projective and hyperbolic spaces must be minimal. This provides their classification, by virtue of a result of Lohnherr and Reckziegel.
In this paper, we give a complete description of the deformation classes of real structures on minimal ruled surfaces. In particular, we show that these classes are determined by the topology of the real structure, which means that real…
This paper deals with a kind of design of a ruled surface. It combines concepts from the fields of computer aided geometric design and kinematics. A dual unit spherical B\'ezier-like curve on the dual unit sphere (DUS) is obtained with…
In this note, we give a slight improvement of a result of A. K\"uronya and V. Lozovanu about higher syzygies on abelian surfaces.
We discuss the relation between the existence of fixed points of the Ruelle operator acting on different Banach spaces, with Sullivan's conjecture in holomorphic dynamics.
We study the non-emptyness of moduli of stable sheaves on an elliptic ruled surface with a nef. anticanonical bundle.
The problem of construction of the surfaces with given sets of the points with horizontal tangential planes is considered. Such considerations are of interest in the problem of computer simulations of the waved ocean surfaces.
We consider the stable ruled surface $S_1$ over an elliptic curve. There is a unique foliation on $S_1$ transverse to the fibration. The minimal self-intersection sections also define a 2-web. We prove that the 4-web defined by the…
In this article we look at a scroll of $PG(6,q)$ that uses a projectivity to rule a conic and a twisted cubic. We show this scroll is a ruled quintic surface $\mathcal V^5_2$, and study its geometric properties. The motivation in studying…
We answer a question of Zadrozny.
We show that a capillary surface in a solid cone, that is, a surface that has constant mean curvature and the boundary of surface meets the boundary of the cone with a constant angle, is radially graphical if the mean curvature is…
This paper deals with skew ruled surfaces in the Euclidean space $\mathbb{E}^{3}$ which are equipped with polar normalizations, that is, relative normalizations such that the relative normal at each point of the ruled surface lies on the…
We give a notion of ordinary Enriques surfaces and their canonical lifts in any positive characteristic, and we prove Torelli-type results for this class of Enriques surfaces.
We count rational points of bounded height on the Cayley ruled cubic surface and interpret the result in the context of general conjectures due to Batyrev and Tschinkel.
Let $f:X \to S$ be a projective morphism of noetherian schemes and let $L$ be an invertible sheaf on $X$. We show that the relative augmented base locus of $L$ coincides with the relative exceptional locus of $L$. We also prove a…