Related papers: On curves and surfaces with projectively equivalen…
Projective structures on curves appear naturally in many areas of mathematics, from extrinsic conformal geometry to analysis, where the main problem is to find qualitative information about the solutions of Hill equations. In this paper, we…
The purpose of this article is to determine explicitly the complete surfaces with parallel mean curvature vector, both in the complex projective plane and the complex hyperbolic plane. The main results are as follows: When the curvature of…
We construct highly singular projective curves and surfaces defined by invariants of primitive complex reflection groups.
We obtain a coarse relationship between geometric intersection numbers of curves and the sum of their subsurface projection distances with explicit quasi-constants. By using this relationship, we give applications in the studies of the…
We provide general inequalities that compare the surface area S(K) of a convex body K in ${\mathbb R}^n$ to the minimal, average or maximal surface area of its hyperplane or lower dimensional projections. We discuss the same questions for…
We give a geometric characterization of certain hypersurfaces of cohomogeneity one in the complex projective and hyperbolic planes. We also obtain some partial classifications of austere hypersurfaces and of Levi-flat hypersurfaces with…
A different proof to a known criterion of derived equivalence implying birationality is given. Derived equivalent smooth projective curves over an algebraically closed field are proved to be isomorphic. A different proof of derived…
We investigate the concept of projective equivalence of connections in supergeometry. To this aim, we propose a definition for (super) geodesics on a supermanifold in which, as in the classical case, they are the projections of the integral…
In this note we address the following kind of question: let X be a smooth, irreducible, projective surface and D a divisor on X$satisfying some sort of positivity hypothesis, then is there some multiple of D depending only on X which is…
In this note, we will illuminate some immediate consequences of work done by Reineke that may prove to be useful in the study of elliptic curves. In particular, we will construct an isomorphism between the category of smooth projective…
We give an explicit construction of a closed curve with constant torsion and everywhere positive curvature. We also discuss the restrictions on closed curves of constant torsion when they are constrained to lie on convex surfaces.
We investigate the projective normality of smooth, linearly normal surfaces of degree 9. All non projectively normal surfaces which are not scrolls over a curve are classified. Results on the projective normality of surface scrolls are also…
We present a necessary and sufficient condition for the topological equivalence of a continuous function on a plane to a projection onto one of coordinates.
Quadratic points of a surface in the projective 3-space are the points which can be exceptionally well approximated by a quadric. They are also singularities of a 3-web in the elliptic part and of a line field in the hyperbolic part of the…
In a previous work of the authors, a result to algorithmically compute the topology types of the level curves of an algebraic surface, is given. From this result, here we derive applications based on level curves to determine some…
A projective rectangle is like a projective plane that has different lengths in two directions. We develop the basic theory of projective rectangles including incidence properties, projective subplanes, configuration counts, a partial…
The paper is a contribution to the conjecture of Kobayashi that the complement of a generic curve in the projective plane is hyperbolic, provided the degree is at least five. Previously the authors treated the cases of two quadrics and a…
We characterize integral homology classes of the product of two projective planes which are representable by a subvariety.
In this paper we give a new and simplified proof of the variational Hodge conjecture for complete intersection cycles on a hypersurface in projective space.
Our purpose in this article is first, following [14], to find the topological upper limits of projections of secant planes to $C^{1}$ surfaces and the topological upper limits of projections of secant hyperplanes to $C^{1}$ hypersurfaces…