相关论文: An example of a very non-movable effective divisor

We study curves of negative self-intersection on algebraic surfaces. We obtain results for smooth complex projective surfaces X on the number of reduced, irreducible curves C of negative self-intersection C^2. The only known examples of…

Metasurfaces represent a powerful paradigm of optical engineering that enables one to control the flow of light across material interfaces. We report on a discovery that metallic metasurfaces of a certain type respond differently to…

We consider the problem of classifying linear systems of hypersurfaces (of a fixed degree) in some projective space up to projective equivalence via geometric invariant theory (GIT). We provide an explicit criterion that solves the problem…

This paper considers the problem of completing assemblies of passive objects in nonconvex environments, cluttered with convex obstacles of unknown position, shape and size that satisfy a specific separation assumption. A differential drive…

We introduce a new general-purpose approach to deep learning on 3D surfaces, based on the insight that a simple diffusion layer is highly effective for spatial communication. The resulting networks are automatically robust to changes in…

Cone spherical metrics, defined on compact Riemann surfaces, are conformal metrics with constant curvature one and finitely many cone singularities. Such a metric is termed \textit{reducible} if a developing map of the metric has monodromy…

A method is introduced for the construction of meshless discretization schemes which preserve Lie symmetries of the differential equations that these schemes approximate. The method exploits the fact that equivariant moving frames provide a…

Finite smooth digraphs, that is, finite directed graphs without sources and sinks, can be partially ordered via pp-constructability. We give a complete description of this poset and, in particular, we prove that it is a distributive…

Three decades ago Cornalba-Harris proved a fundamental positivity result for divisor classes associated to families of stable curves. In this paper we establish an analogous positivity result for divisor classes associated to families of…

Here we investigate the property of effectivity for adjoint divisors. Among others, we prove the following results: (i) A normal projective variety $X$ with at most canonical singularities is uniruled if and only if for each very ample…

Suppose X is a projective variety, which needs not be smooth, and L an ample divisor on X. We show that there are integers c and b such that for any nonnegative integer p, L^d is normally generated and embeds X as a variety who defining…

Understanding the scene in which an autonomous robot operates is critical for its competent functioning. Such scene comprehension necessitates recognizing instances of traffic participants along with general scene semantics which can be…

We investigate properties and describe examples of tilt-stable objects on a smooth complex projective threefold. We give a structure theorem on slope semistable sheaves of vanishing discriminant, and describe certain Chern classes for which…

In this paper we give a negative answer to the question posed in [15, Open Question 2.1] about possible gains of integrability of determinants of divergence-free, non-negative definite matrix-fields. We also analyze the case in which the…

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…

This paper proposed a retinal image segmentation method based on conditional Generative Adversarial Network (cGAN) to segment optic disc. The proposed model consists of two successive networks: generator and discriminator. The generator…

Generative deep learning systems offer powerful tools for artefact generation, given their ability to model distributions of data and generate high-fidelity results. In the context of computational creativity, however, a major shortcoming…

We construct a linearly normal smooth rational surface S of degree 11 and sectional genus 8 in the projective fivespace. Surfaces satisfying these numerical invariants are special, in the sense that $h^1(\mathscr{O}_S(1))>0$. Our…

The divisor graph is the non oriented graph whose vertices are the positive integers, and edges are the {a,b} such that a divides b. Let P(n) be the largest prime factor of n, S(x,y) = {n<=x: P(n) <= y} and Psi(x,y) = Card S(x,y). Let…

Employing large intelligent surfaces (LISs) is a promising solution for improving the coverage and rate of future wireless systems. These surfaces comprise a massive number of nearly-passive elements that interact with the incident signals,…