Grassmann cactus variety and socle dimension
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.
Authors
- Jarosław Buczyński (ORCID: https://orcid.org/0000-0002-9811-4238)
- Weronika Buczyńska (ORCID: https://orcid.org/0000-0002-7336-3676)
- Maciej Gałązka (ORCID: https://orcid.org/0000-0002-1845-7266)
Institutions
- Warsaw University of Technology (PL)
- Warsaw University of Life Sciences (PL)
- Daegu Gyeongbuk Institute of Science and Technology (KR)
- Institute of Mathematics (PL)
- Polish Academy of Sciences (PL)
Publication Details
- Journal
- Bulletin of the Polish Academy of Sciences Mathematics
- Published
- 2025-09-12
- DOI
- https://doi.org/10.4064/ba250729-24-8
- Primary Topic
- Leaf Properties and Growth Measurement
- Type
- article
- Field-Weighted Citation Impact
- 0.00