A Schubert Catalogue

Schubert functors and Schubert polynomials

We construct a family of functors assigning an R-module to a flag of R-modules, where R is a commutative ring. As particular instances, we get flagged Schur functors and Schubert functors, the latter family being indexed by permutations. We identify Schubert functors for vexillary permutations with some flagged Schur functors, thus establishing a functorial analogue of a theorem from [6] and [1...

Contemporary Schubert Calculus and Schubert Geometry

Schubert calculus refers to the calculus of enumerative geometry, which is the art of counting geometric figures determined by given incidence conditions. For example, how many lines in projective 3-space meet four given lines? This was developed in the 19th century and presented in the classic treatise ”Kälkul der abzählanden Geometrie” by Herman Cäser Hannibal Schubert in 1879. Schubert, Pier...

A catalogue of singularities

This paper is an attempt to classify finite-time singularities of PDEs. Most of the problems considered describe free-surface flows, which are easily observed experimentally. We consider problems where the singularity occurs at a point, and where typical scales of the solution shrink to zero as the singularity is approached. Upon a similarity transformation, exact self-similar behaviour is mapp...

Skew Schubert

A catalogue of symbiotic stars

We present a new catalogue of symbiotic stars. In our list we include 188 symbiotic stars as well as 28 objects suspected of being symbiotic. For each star, we present basic observational material: coordinates, V and K magnitudes, ultraviolet (UV), infrared (IR), X-ray and radio observations. We also list the spectral type of the cool component, the maximum ionization potential observed, refere...