English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Consider the Hilbert scheme of points on a higher dimensional affine space. Its component is  elementary  if it parameterizes irreducible subschemes. We characterize reduced elementary components in terms of tangent spaces and provide a computationally efficient way of finding such components. As an example, we find an infinite family of elementary and generically smooth components on the affine four‐space. We analyse singularities and formulate a conjecture which would imply the non‐reducedness of the Hilbert scheme. Our main tool is a generalization of the Białynicki–Birula decomposition for this singular scheme.

Elementary components of Hilbert schemes of points