Related papers: Desingularization in Computational Applications an…
We survey the role of symmetry in diffeomorphic registration of landmarks, curves, surfaces, images and higher-order data. The infinite dimensional problem of finding correspondences between objects can for a range of concrete data types be…
We develop a new symbolic-numeric algorithm for the certification of singular isolated points, using their associated local ring structure and certified numerical computations. An improvement of an existing method to compute inverse systems…
We present a proof of embedded desingularization for closed subschemes which does not make use of Hilbert-Samuel function and avoids Hironaka's notion of normal flatness. This proof, already sketched in [A course on constructive…
We reformulate the analysis of singularities of Feynman integrals in a way that can be practically applied to perturbative computations in the Standard Model in dimensional regularization. After highlighting issues in the textbook treatment…
We find formulas for the birational maps from a Kummer surface K and its dual K^* to their common minimal desingularization S. We show how the nodes of K blow up. Then we give a description of the group of linear automorphisms of S.
We enumerate plane complex algebraic curves of a given degree with one singularity of any given topological type. Our approach is to compute the homology classes of the corresponding equisingular strata in the parameter spaces of plane…
We compute the limit of tangents of an arbitrary surface. We obtain as a byproduct an embedded version of Jung's desingularization theorem for surface singularities with finite limits of tangents.
Every polyhedral cone can be described either by its facets or by its extreme rays. Computation of one description from the other is a problem that can be very complex, i.e. one encounter the combinatorial explosion. We present here several…
Topological physics desires stable methods to measure the polarization singularities in optical vector fields. Here a periodic plasmonic metasurface is proposed to perform divergence computation of vectorial paraxial beams. We design such…
This is a survey on Zariski equisingularity. We recall its definition, main properties, and a variety of applications in Algebraic Geometry and Singularity Theory. In the first part of this survey, we consider Zariski equisingular families…
We show that Ore operators can be desingularized by calculating a least common left multiple with a random operator of appropriate order. Our result generalizes a classical result about apparent singularities of linear differential…
The algebraic method of singular reduction is applied for non regular group action on manifolds which provides singular symplectic spaces. The problem of deformation quantization of the singular surfaces is the focus. For some examples of…
We introduce the notion of a simultaneous categorical resolution of singularities, a categorical version of simultaneous resolutions of rational double points of surface degenerations. Furthermore, we suggest a construction of simultaneous…
This survey provides an overview of common applications, both implicit and explicit, of "tensors" and "tensor products" in the fields of data science and statistics. One goal is to reconcile seemingly distinct usages of the term "tensor" in…
We utilise the two principles of decoupling introduced in arXiv:2407.16108 to prove the following conditional result: assuming uniform decoupling for graphs of polynomials in all dimensions with identically zero Gaussian curvature, we can…
The dual complex associated to a resolution of singularities generalizes the notion of a resolution graph of a surface singularity to any dimension. We show that homotopy type of the dual complex is an invariant of an isolated singularity.
The aim of these notes is to present an accessible overview of some topics in classical algebraic geometry which have applications to aspects of discrete integrable systems. Precisely, we focus on surface theory on the algebraic geometry…
This paper presents a method for mathematical modelling of surfaces conditioned on empirical data. It is based on solving a discrete biharmonic equation over a domain with given inner point and inner curve data. The inner curve data is used…
Geometry processing presents a variety of difficult numerical problems, each seeming to require its own tailored solution. This breadth is largely due to the expansive list of geometric primitives, e.g., splines, triangles, and hexahedra,…
We describe a new algorithm to compute the geometric intersection number between two curves, given as edge vectors on an ideal triangulation. Most importantly, this algorithm runs in polynomial time in the bit-size of the two edge vectors.…