On the construction of k-regular maps to Grassmannians via algebras of socle dimension two

On the Hilbert function of Artinian local complete intersections of codimension three

“…For n = 3 it is irreducible for d ≤ 11, see [40] and reducible for d ≥ 78, see [69,Example 4.3], see also §2.3. The punctual Hilbert scheme for n ≥ 4 is reducible when d ≥ 8 and irreducible for d ≤ 7, see [99] and also [80,Proposition 2. While the Hilbert scheme of A 3 was investigated for many years, it seems that the Gorenstein locus in A 4 received less attention. It is however important for applications to secant varieties, see [18,20].…”

“…However, local complete intersections are not necessarily limits of curvilinear schemes [68] 3 . Perhaps the newly introduced method of Bia lynicki-Birula slicing [80] could be of use for this problem.…”