Related papers: Extactic divisors for webs and lines on projective…
We characterize surface-plasmon polaritons at lossy planar interfaces between one dispersive and one nondispersive linear isotropic homogeneous media, i.e., materials or metamaterials. Specifically we solve Maxwell's equations to obtain…
Discretization of flow in fractured porous media commonly lead to large systems of linear equations that require dedicated solvers. In this work, we develop an efficient linear solver and its practical implementation for mixed-dimensional…
A degeneration of a smooth projective curve to a strongly stable curve gives rise to a specialization map from divisors on curves to divisors on graphs. In this paper we show that this specialization behaves well under the presence of real…
A line field on a manifold is a smooth map which assigns a tangent line to all but a finite number of points of the manifold. As such, it can be seen as a generalization of vector fields. They model a number of geometric and physical…
Given a connected smooth projective surface X over the complex numbers, together with a simple normal crossings divisor D on it, we study finite normal covers Y of X that are unramified outside D. Given moreover a fibration of X onto a…
Motivated by a conjecture of Xiao, we study supporting divisors of fibred surfaces. On the one hand, after developing a formalism to treat one-dimensional families of varieties of any dimension, we give a structure theorem for fibred…
We investigate the interplay between linear systems on curves and graphs in the context of specialization of divisors on an arithmetic surface. We also provide some applications of our results to graph theory, arithmetic geometry, and…
We study framed translation surfaces corresponding to meromorphic differentials on compact Riemann surfaces, for which a horizontal separatrix is marked for each pole or zero. Such geometric structures naturally appear when studying flat…
Our recent work identifies material surfaces in incompressible flows that extremize the transport of an arbitrary, weakly diffusive scalar field relative to neighboring surfaces. Such barriers and enhancers of transport can be located…
We give a simple analytic criterion which characterizes linearizable 1-codimensional webs. Then we give an invariant geometrical interpretation of it, in term of projective connection. We explain then how our approach allows to study…
We study effective divisors $D$ on surfaces with $H^0(\mathcal O_D)=k$ and $H^1(\mathcal O_D)=H^0(\mathcal O_D(D))=0$. We give a numerical criterion for such divisors, following a general investigation of negativity, rigidity and…
For a smooth projective curve, the cycles of subordinate or, more generally, secant divisors to a given linear series are among some of the most studied objects in classical enumerative geometry. We consider the intersection of two such…
We completely describe the Fano scheme of lines for a projective toric surface in terms of the geometry of the corresponding lattice polygon.
We study effective versions of unlikely intersections of images of torsion points of elliptic curves on the projective line.
Using group theoretic and topological concepts, together with tunneling phenomena, we geometrically design interfacial wave networks that contain splitters which partition energy in 2, 3, 4 or 5 directions. This enriches the valleytronics…
An efficient computer algorithm is described for the perspective drawing of a wide class of surfaces. The class includes surfaces corresponding lo single-valued, continuous functions which are defined over rectangular domains. The algorithm…
The first part of this note contains a review of basic properties of the variety of lines contained in an embedded projective variety and passing through a general point. In particular we provide a detailed proof that for varieties defined…
We study spin structures on Riemann and Klein surfaces in terms of divisors. In particular, we take a closer look at spin structures on hyperelliptic and $p$-gonal surfaces defined by divisors supported on their branch points. Moreover, we…
This is a detailed study of the infinitesimal variation of the variety of lines through a point of a low degree hypersurface in pro jective space. The motion is governed by a system of partial differential equations which we describe…
We consider fibrations by affine lines on smooth affine surfaces obtained as complements of smooth rational curves $B$ in smooth projective surfaces $X$ defined over an algebraically closed field of characteristic zero. We observe that…