Related papers: Ruled quartic surfaces, models and classification
Let V be a plane smooth cubic curve over a finitely generated field k. The Mordell-Weil theorem for V states that there is a finite subset P \subset V(k) such that the whole V(k) can be obtained from P by drawing secants and tangents…
We study embeddability of rational ruled surfaces as symplectic hyperplane sections into closed integral symplectic manifolds. From this we obtain results on Stein fillability of Boothby--Wang bundles over rational ruled surfaces.
This paper deals with skew ruled surfaces $\varPhi$ in the Euclidean space $\mathbb{E}^{3}$ which are right normalized, that is they are equipped with relative normalizations, whose support function is of the form $q(u,v) = \frac{f(u) +…
A fake quadric is a smooth projective surface that has the same rational cohomology as a smooth quadric surface but is not biholomorphic to one. We provide an explicit classification of all irreducible fake quadrics according to the…
We give a bound on the number of isolated, essential singularities of determinantal quartic surfaces in 3-space. We also provide examples of different configurations of real singularities on quartic surfaces with a definite Hermitian…
A new construction is presented of scalar-flat Kaehler metrics on non-minimal ruled surfaces. The method is based on the resolution of singularities of orbifold ruled surfaces which are closely related to rank-2 parabolically stable…
A class of surfaces-graphs in a Riemannian 3-space with a prescribed projection of one field of principal directions onto a surface $\Pi$ is considered. A problem of determination of such surfaces when both principal curvatures are given…
Edge-to-edge tilings of the sphere by congruent quadrilaterals are completely classified in a series of three papers. This second one applies the powerful tool of trigonometric Diophantine equations to classify the case of…
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 text grew up from the notes of a graduate course I gave at the University of Roma ``Tor Vergata'' in the academic year 2018--19. The subject is the classification of complex algebraic surfaces following Mori's theory. It includes the…
Let R be a noetherian connected graded domain of Gelfand-Kirillov dimension 3 over an uncountable algebraically closed field. Suppose that the graded quotient ring of R is a skew-Laurent ring over a field; we say that R is a birationally…
A series of ceramic artworks are presented, inspired by the author's research connecting theoretical physics to the beautiful theory of Riemann surfaces. More specifically the research is related to the classification of curves on the…
We investigate the universal Severi variety of rational curves on K3 surfaces, which parametrises irreducible rational curves in a fixed class on varying K3 surfaces of fixed genus. We investigate the conjecuted irreducibility of this space…
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…
We prove a new classification result for (CR) rational maps from the unit sphere in some ${\mathbb C}^n$ to the unit sphere in ${\mathbb C}^N$. To so so, we work at the level of Hermitian forms, and we introduce ancestors and descendants.
Surfaces and curves play an important role in geometric design. In recent years, problem of finding a surface passing through a given curve have attracted much interest. In the present paper, we propose a new method to construct a surface…
Log-symplectic structures are Poisson structures that are determined by a symplectic form with logarithmic singularities. We construct moduli spaces of curves with values in a log-symplectic manifold. Among the applications, we classify…
We develop an essentially algebraic method to study biharmonic curves into an implicit surface. Although our method is rather general, it is especially suitable to study curves into surfaces defined by a polynomial equation: in particular,…
In this study, we give the dual characterizations of Mannheim offsets of the ruled surface in terms of their integral invariants and the new characterization of the Mannheim offsets of developable surface. Furthermore, we obtain the…
Quadratic residue patterns modulo a prime are studied since 19th century. In the first part we extend existing results on the number of consecutive $\ell$-tuples of quadratic residues, studying corresponding algebraic curves and their…