5 papers · 1 filter
General symmetric ideals
Alexandra Seceleanu, Liana Şega
We investigate the structure and properties of symmetric ideals generated by general forms in the polynomial ring under the natural action of the symmetric group. This work signifi…
Lefschetz properties through a topological lens
Alexandra Seceleanu
These lecture notes were prepared for the Lefschetz Preparatory School, a graduate summer course held in Krakow, May 6-10, 2024. They present the story of the algebraic Lefschetz p…
Betti numbers for connected sums of graded Gorenstein artinian algebras
Nasrin Altafi, Roberta Di Gennaro, Federico Galetto +5
The connected sum construction, which takes as input Gorenstein rings and produces new Gorenstein rings, can be considered as an algebraic analogue for the topological construction…
The combinatorial structure of symmetric strongly shifted ideals
Alessandra Costantini, Alexandra Seceleanu
Symmetric strongly shifted ideals are a class of monomial ideals which come equipped with an action of the symmetric group and are analogous to the well-studied class of strongly s…
A homological criterion for the containment between symbolic and ordinary powers for some ideals of points in
Alexandra Seceleanu
We establish a criterion for the (failure of) the containment for 3-generated ideals defining reduced sets of points in . Our criterion arise…