Grassmann cactus variety and socle dimension
Bulletin Polish Acad. Sci. Math.
MSC: Primary 14A15; Secondary 13H10, 14D99, 14N07
DOI: 10.4064/ba250729-24-8
Published online: 12 September 2025
Abstract
Grassmann cactus variety is a common generalisation of Grassmann secant variety and cactus variety. In their definitions one considers the vector spaces of fixed dimension that are contained in the linear span of some finite schemes. We prove that to characterise Grassmann cactus varieties it is enough to use finite schemes that locally have low socle dimension. This motivates the study of parameter spaces of such schemes and simplifies calculations of examples of Grassmann cactus varieties.
