Related papers: A conjecture on special linear systems of P^3
This paper presents a type theory in which it is possible to directly manipulate $n$-dimensional cubes (points, lines, squares, cubes, etc.) based on an interpretation of dependent type theory in a cubical set model. This enables new ways…
The melting transition of a system of hard cubes is studied numerically both in the case of freely rotating cubes and when there is a fixed orientation of the particles (parallel cubes). It is shown that freelly rotating cubes melt through…
Differential systems with a Fuchsian linear part are studied in regions including all the singularities in the complex plane of these equations. Such systems are not necessarily analytically equivalent to their linear part (they are not…
By defining a fat point subscheme of $P^2$ to be a 0-dimensional subscheme defined by a sheaf of integrally closed ideals one extends the notion of fat point subschemes to allow infinitely near points. With this notion of fat points, this…
A Cremona transformation is a birational self-map of the projective space $ \mathbb{P}^{n} $. Cremona transformations of $ \mathbb{P}^{n} $ form a group and this group has a rational action on subvarieties of $ \mathbb{P}^{n} $ and hence on…
We consider a continuous-time linear time-invariant dynamical system that admits an invariant cone. For the case of a self-dual and homogeneous cone we show that if the system is asymptotically stable then it admits a quadratic Lyapunov…
In this paper, we develop a representation-theoretic formulation of discrete-time linear systems. We show that such systems are naturally viewed as representations of time groups acting on vector spaces, thereby endowing the state space…
We discuss the role of pseudo-fermions in the analysis of some two-dimensional models, recently introduced in connection with non self-adjoint hamiltonians. Among other aspects, we discuss the appearance of exceptional points in connection…
We study linearizability of actions of finite groups on singular cubic threefolds, using cohomological tools, intermediate Jacobians, Burnside invariants, and the equivariant Minimal Model Program.
We develop a theory of $n \times n$-matrix Riemann-Hilbert problems for a class of jump contours and jump matrices of low regularity. Our basic assumption is that the contour $\Gamma$ is a finite union of simple closed Carleson curves in…
We describe all special curves in the parameter space of complex cubic polynomials, that is all algebraic irreducible curves containing infinitely many post-critically finite polynomials. This solves in a strong form a conjecture by Baker…
We report an open three-state perturbed system with quasi-statically varying Hamiltonian depending on the topological parameters. The effective system hosts two second order exceptional points (EP2s). Here a third order exceptional point…
A birational transformation f: P^n --> Z, where Z is a nonsingular variety of Picard number 1, is called a special birational transformation of type (a, b) if f is given by a linear system of degree a, its inverse is given by a linear…
Exceptional orthogonal polynomial systems (X-OPS) arise as eigenfunctions of Sturm-Liouville problems and generalize in this sense the classical families of Hermite, Laguerre and Jacobi. They also generalize the family of CPRS orthogonal…
We consider the open problem of determining the graded Betti numbers for fat point subschemes supported at general points of the projective plane. We relate this problem to the open geometric problem of determining the splitting type of the…
In this manuscript, we describe a new configurational bias Monte Carlo technique for the simulation of peptides. We focus on the biologically relevant cases of linear and cyclic peptides. Our approach leads to an efficient,…
The main result of this paper is a probabilistic construction of finite rigid structures. It yields a finitely axiomatizable class of finite rigid structures where no L^omega_{infty, omega} formula with counting quantifiers defines a linear…
We develop a purely combinatorial theory of limit linear series on metric graphs. This will be based on the formalisms of hypercube rank functions and slope structures. We provide a full classification of combinatorial limit linear series…
We prove that the linear system of hypersurfaces in P^3 of degree d, 14 <= d <= 40, with double, triple and quadruple points in general position are non-special. This solves the cases that have not been completed in a paper by E. Ballico…
Quantum deformations of sets of points of the real and the complexified projective line are constructed. These deformations depend on the deformation parameter q and certain further parameters \lambda_{ij}. The deformations for which the…