Related papers: Obstructions to deforming space curves lying on a …

We determine all the Kummer-surface-type Calabi-Yau (CY) 3-folds, i.e., those $\hat{T/G}$ which are resolutions of 3-torus-orbifolds $T/G$ with only isolated singularities. There are only two such CY spaces: one with $G= \ZZ_3$ and $T$…

We consider flat families of reduced curves on a smooth surface S such that each member C has the same number of singularities of fixed singularity types and the corresponding (locally closed) subscheme H of the Hilbert scheme of S. We are…

In a previous paper, the first two named authors established an isomorphism between the moduli space of framed flags of sheaves on the projective plane and the moduli space of stable representations of a certain quiver. In the present note,…

Let $H$ be the Hilbert scheme of curves in complex projective $3$-space, with $d\geq 3$ and genus $g \leq (d-2)^2/4$. A complete, explicit description of the cone of curves and the ample cone of $H$ is given. From this, partial results on…

The role of curvature in relation with Lie algebra contractions of the pseudo-ortogonal algebras so(p,q) is fully described by considering some associated symmetrical homogeneous spaces of constant curvature within a Cayley-Klein framework.…

A quantum sl(2,R) coalgebra (with deformation parameter z) is shown to underly the construction of superintegrable Kepler potentials on 3D spaces of variable and constant curvature, that include the classical spherical, hyperbolic and…

Let F be a smooth surface in a smooth projective threefold T, and let X=2F be the first infinitesimal neighborhood of X in T. A locally Cohen-Macaulay curve C in X gives rise to two effective divisors on F, namely the curve part P of the…

Classification of curves in a projective space occupies minds of many mathematicians. First step in doing so is classification of curves on a given surface. This brings us to consideration of the nonsingular Del Pezzo Surface in $P^4_k.$ We…

Biconservative surfaces of Riemannian 3-space forms $N^3(\rho)$, are either constant mean curvature (CMC) surfaces or rotational linear Weingarten surfaces verifying the relation $3\kappa_1+\kappa_2=0$ between their principal curvatures…

In this study, we define some new types of ruled surfaces called slant ruled surfaces. We give some characterizations for a regular ruled surface to be a slant ruled surface in Euclidean 3- space. We show that if the slant ruled surface is…

We study maximal families W of the Hilbert scheme, H(d,g)_{sc}, of smooth connected space curves whose general curve C lies on a smooth surface S of degree s. We give conditions on C under which W is a generically smooth component of…

In this paper, we study the deformation theory of degenerate algebraic curves on singular varieties which appear as the degenerate limit of families of varieties. For this purpose, we systematically develop a new method to calculate the…

We study Lagrangian points on smooth holomorphic curves in T${\mathbb P}^1$ equipped with a natural neutral K\"ahler structure, and prove that they must form real curves. By virtue of the identification of T${\mathbb P}^1$ with the space…

In this paper we characterize concircular helices in $R^3$ by means of a differential equation involving their curvature and torsion. We find a full description of concircular surfaces in $R^3$ as a special family of ruled surfaces, and we…

Motivated by a question of Erd\H{o}s on blocking sets in a projective plane that intersect every line only a few times, several authors have used unions of algebraic curves to construct such sets in $\mathbb{P}^2(\mathbb{F}_q)$. In this…

The boundary of the convex hull of a compact algebraic curve in real 3-space defines a real algebraic surface. For general curves, that boundary surface is reducible, consisting of tritangent planes and a scroll of stationary bisecants. We…

We will use toric degenerations of the projective plane ${{\mathbb{P}}^ 2}$ to give a new proof of the triple points interpolation problems in the projective plane. We also give a complete list of toric surfaces that are useful as…

In this note, we develop a condition on a closed curve on a surface or in a 3-manifold that implies that the curve has the property that its length function on the space of all hyperbolic structures on the surface or 3-manifold completely…

In this paper are studied the nets of principal curvature lines on surfaces embedded in Euclidean $3-$space near their end points, at which the surfaces tend to infinity. This is a natural complement and extension to smooth surfaces of the…

The main theorem of "S. J. Kov\'acs: The cone of curves of a K3 surface, Math. Ann. 300 (1994), no. 4, 681-691" is proved in arbitrary characteristic. The proof is essentially the same as in the original paper where it was stated only over…