Related papers: A ruled quintic surface in $PG(6,q)$
We show the dominance of the restriction map from a moduli space of stable sheaves on the projective plane to the Coble quartic. With the dominance and the interpretation of a stable sheaf on the plane in terms of the hyperplane…
Given an odd representation of the absolute Galois group of Q onto PGL(2,3) and a positive integer N, there exists a twisted modular curve defined over Q whose rational points classify the quadratic Q-curves of degree N realizing the…
In this paper we study combinatorial invariants of the equivalence classes of pencils of cubics on $\mathrm{PG}(1,q)$, for $q$ odd and $q$ not divisible by 3. These equivalence classes are considered as orbits of lines in…
It is well-known that there exists a bijection between the set of lines of the projective 3-dimensional space $P^3$ and all real points of the so-called Pl\"ucker quadric $\Psi$. Moreover one can identify each point of the Pl\"ucker…
Let A=k+A_1+A_2.... be a connected graded, noetherian k-algebra that is generated in degree one over an algebraically closed field k. Suppose that the graded quotient ring Q(A) has the form Q(A)=k(Y)[t,t^{-1},sigma], where sigma is an…
The purposes of this article are threefold. First, to determine numerically when an arbitrary blowup of a smooth surface is smooth. We show the surface is smooth if and only if certain rational parameters involving log discrepancy and…
We investigate birational properties of hypersurfaces of degree $6$ in the weighted projective space $\mathbf{P}(1,1,2,2,3)$. In particular, we prove that any such quasi-smooth hypersurface is not rational.
We study nodal quintic surfaces with an even set of 16 nodes as analogues of singular Kummer surfaces. The interpretation of the natural double cover of an even 16-nodal quintic as a certain Fano variety of lines could be viewed as a…
A smooth ruled surface in 4-space has only parabolic points or inflection points of real type. We show, by means of contact with transverse planes, that at a parabolic point, there exist two tangent directions determining two planes along…
We study structures of embedded projective manifolds swept out by cubic varieties. We show if an embedded projective manifold is swept out by high-dimensional smooth cubic hypersurfaces, then it admits an extremal contraction which is a…
We study the geometry and codes of quartic surfaces with many cusps. We apply Gr\"obner bases to find examples of various configurations of cusps on quartics.
The Peirce quincuncial projection is a mapping of the surface of a sphere to the interior of a square. It is a conformal map except for four points on the equator. These points of non-conformality cause significant artifacts in photographic…
In this paper we provide, first, a general symbolic algorithm for computing the symmetries of a given rational surface, based on the classical differential invariants of surfaces, i.e. Gauss curvature and mean curvature. In practice, the…
In this paper we classify certain special ruled surfaces in $\R^3$ under the general theorem of characterization of constant angle surfaces. We study the tangent developable and conical surfaces from the point of view the constant angle…
In this paper we study the intersection theory on surfaces with abelian quotient singularities and we derive properties of quotients of weighted projective planes. We also use this theory to study weighted blow-ups in order to construct…
Let X be a scroll over a rational surface. We construct a linear system of surfaces in P^3 yielding a birational map from P^3 to X. We apply this construction to the scrolls of Bordiga and Palatini.
We investigate ruled surfaces in 3d Riemannian manifolds, i.e., surfaces foliated by geodesics. In 3d space forms, we find the striction curve, distribution parameter, and the first and second fundamental forms, from which we obtain the…
In this note we prove that the Beilinson conjecture holds for certain examples of K3 surfaces over $\bar {\mathbb{Q}}$ equipped with an involution, when the quotient of the surface by the involution is the projective plane branched along a…
In this paper we study topological surfaces as gridded surfaces in the 2-dimensional scaffolding of cubic honeycombs in Euclidean and hyperbolic spaces.
A rational elliptic surface with section is a smooth, rational, complex, projective surface $\mathcal{X}$ that admits a relatively minimal fibration $f: \mathcal{X}\longrightarrow \bbP^1$ such that its general fibre is a smooth irreducible…