Related papers: Explicit Superconic Curves
Many well-known combinatorial optimization problems can be stated over the set of acyclic orientations of an undirected graph. For example, acyclic orientations with certain diameter constraints are closely related to the optimal solutions…
Recently Fukasawa, Homma and Kim introduced and studied certain projective singular curves over $\mathbb {F}_q$ with many extremal properties. Here we extend their definition to more general non-rational curves.
We develop a geometric mechanism to prove the existence of orbits that drift along a prescribed sequence of cylinders, under some general conditions on the dynamics. This mechanism can be used to prove the existence of Arnold diffusion for…
We present some new ideas on how to design analogue models of quantum fields living in curved spacetimes using ultra-cold atoms in optical lattices. We discuss various types of static and dynamical curved spacetimes achievable by simple…
A strict confluent (SC) graph drawing is a drawing of a graph with vertices as points in the plane, where vertex adjacencies are represented not by individual curves but rather by unique smooth paths through a planar system of junctions and…
We elaborate on the notion of generalized tomograms, both in the classical and quantum domains. We construct a scheme of star-products of thick tomographic symbols and obtain in explicit form the kernels of classical and quantum generalized…
Creative telescoping applied to a bivariate proper hypergeometric term produces linear recurrence operators with polynomial coefficients, called telescopers. We provide bounds for the degrees of the polynomials appearing in these operators.…
Let ${\mathcal {B}}$ be a reducible reduced plane curve. We introduce a new point of view to study the topology of $(\PP^2, {\mathcal {B}})$ via Galois covers and Alexander polynomials. We show its effectiveness through examples of Zariski…
In this paper, we prove a theorem on tight paths in convex geometric hypergraphs, which is asymptotically sharp in infinitely many cases. Our geometric theorem is a common generalization of early results of Hopf and Pannwitz, Sutherland,…
We explore the concept of projections of syzygies and prove two new technical results; we firstly give a precise characterization of syzygy schemes in terms of their projections, secondly, we prove a converse to Aprodu's Projection Theorem.…
Selected stories about the life of A. L. Onishchik, and a review of his contribution to the classification of non-split supermanifolds, in particular, supercurves a.k.a. superstrings; his editorial and educational work. A brief overview of…
An algebraic system is proposed that represent surface cobordisms in thickened surfaces. Module and comodule structures over Frobenius algebras are used for representing essential curves. The proposed structure gives a unified algebraic…
We give a geometrical characterization of the ideal of quadrics containing a canonical curve with an involution. This implies to study involutions of rational normal scrolls and Veronese surfaces.
A hyperbolic algebraic curve is a bounded subset of an algebraic set. We study the function theory and functional analytic aspects of these sets. We show that their function theory can be described by finite codimensional subalgebras of the…
In this article, we functorially associate definable sets to $k$-analytic curves, and definable maps to analytic morphisms between them, for a large class of $k$-analytic curves. Given a $k$-analytic curve $X$, our association allows us to…
This thesis investigates cusp cross-sections of arithmetic real, complex, and quaternionic hyperbolic $n$--orbifolds. We give a smooth classification of these submanifolds and analyze their induced geometry. One of the primary tools is a…
We introduce supersymmetric indices for four-dimensional gauge theories defined on $\mathscr O \times S^1$, where $\mathscr O $ is a circle bundle over the weighted complex projective line informally known as spindle. Trivial fibrations…
A hyperbolic framed curve is a smooth curve with a moving frame in hyperbolic 3-space. It may have singularities. By using this moving frame, we can investigate the differential geometry properties of curves, even at singular points. In…
We define analytic maps between super Riemann surfaces which extend the notion of branched covering maps to a supersymmetric setting. We show that these super covering maps appear naturally both in symmetric product orbifolds of…
By studying $\mathbb{A}^1$-curves on varieties, we propose a geometric approach to strong approximation problem over function fields of complex curves. We prove that strong approximation holds for smooth, low degree affine complete…