Abstract In this article, we give the structure of codimension one foliations with canonical singularities and numerically trivial class on varieties klt singularities. Building recent works Spicer, Cascini—Spicer Spicer—Svaldi, then describe birational geometry rank two numerical dimension zero complex projective three-folds.

Consider a sub-Riemannian geometry (U, D, g) where U is a neighborhood at 0 in IRn, D is a rank-2 smooth (C∞ or Cω) distribution and g is a smooth metric on D. The objective of this article is to explain the role of abnormal minimizers in SR-geometry. It is based on the analysis of the Martinet SR-geometry.

We provide a geometric characterization of k -dimensional F q m -linear sum-rank metric codes as tuples -subspaces . then use this to study one-weight in the metric. This leads us extend family linearized Reed-Solomon order obtain doubly-extended version them. prove that these are still maximum distance (MSRD) and, when = 2 , they one-weight, Hamming-metric case. focus on constant rank-profile ...

Low-rank matrix approximation, which aims to construct a low-rank matrix from an observation, has received much attention recently. An efficient method to solve this problem is to convert the problem of rank minimization into a nuclear norm minimization problem. However, soft-thresholding of singular values leads to the elimination of important information about the sensed matrix. Weighted nucl...