Related papers: Goppa Duality for Surfaces
We classify GL(2,R) invariant point markings over components of strata of Abelian differentials. Such point markings exist only when the component is hyperelliptic and arise from marking Weierstrass points or two points exchanged by the…
We present a geometric realization of the duality between skeleta in $T^*\mathbb P^n$ and collars of local surfaces. Such duality is predicted by combining two auxiliary types of duality: on one side, symplectic duality between $T^*\mathbb…
We describe a general method to determine dualities between supersymmetric 5d gauge theories. The method is based on performing local S-dualities in the geometry associated to the gauge theory. We find that often a duality can be obtained…
The Connes formula giving the dual description for the distance between points of a Riemannian manifold is extended to the Lorentzian case. It resulted that its validity essentially depends on the global structure of spacetime. The duality…
We introduce an alternative formalization of curved spaces in which the concept of a pointwise affine space, as defined here, replaces that of a manifold. New or modified definitions of familiar notions from differential geometry such as…
We extend the notion of self-duality to spaces built from a set of representations of the Lorentz group with bosonic or fermionic behaviour, not having the traditional spin-one upper-bound of super Minkowski space. The generalized…
A theta surface in affine 3-space is the zero set of a Riemann theta function in genus 3. This includes surfaces arising from special plane quartics that are singular or reducible. Lie and Poincar\'e showed that theta surfaces are precisely…
Using the method of moving frames we analyze the algebra of differential invariants for surfaces in three-dimensional affine geometry. For elliptic, hyperbolic, and parabolic points, we show that if the algebra of differential invariants is…
In the prequel to this paper, two versions of Le Potier's strange duality conjecture for sheaves over abelian surfaces were studied. A third version is considered here. In the current setup, the isomorphism involves moduli spaces of sheaves…
Consider a normal complex analytic surface singularity. It is called Gorenstein if the canonical line bundle is holomorphically trivial in some punctured neighborhood of the singular point and is called numerically Gorenstein if this line…
We prove the Lipman-Zariski conjecture for complex surface singularities with $p_g - g - b \le 2$. Here $p_g$ is the geometric genus, $g$ is the sum of the genera of the exceptional curves and $b$ is the first Betti number of the dual…
We study a new discretization of the Gaussian curvature for polyhedral surfaces. This discrete Gaussian curvature is defined on each conical singularity of a polyhedral surface as the quotient of the angle defect and the area of the Voronoi…
The purpose of the present article is the study of duals of functional codes on algebraic surfaces. We give a direct geometrical description of them, using differentials. Even if this geometrical description is less trivial, it can be…
The deviation of a general convex body with twice differentiable boundary and an arbitrarily positioned polytope with a given number of vertices is studied. The paper considers the case where the deviation is measured in terms of the…
It is a classical result in matrix algebra that any square matrix over a field can be conjugated to its transpose by a symmetric matrix. For $F$ a non-Archimedean local field, Tupan used this to give an elementary proof that transpose…
The subject of limit curve theorems in Lorentzian geometry is reviewed. A general limit curve theorem is formulated which includes the case of converging curves with endpoints and the case in which the limit points assigned since the…
Total five different types of translation surfaces, based upon planarity of translating curves and the absolute figure, arise in a Galilean 3-space. Excepting the type in which both of translating curves are non-planar we obtain these…
A criterion for the existence of a plane model of an algebraic curve such that the Galois closures of projections from two points are the same is presented. As an application, it is proved that the Hermitian curve in positive characteristic…
In this paper we obtain an explicit formula for the number of curves in a compact complex surface $X$ (passing through the right number of generic points), that has up to one node and one singularity of codimension $k$, provided the total…
What is the shape of the free resolution of the ideal of a general set of points in P^r? This question is central to the programme of connecting the geometry of point sets in projective space with the structure of the free resolutions of…