4 papers · 2 filters
On the perturbations of Noetherian local domains
Hong Duc Nguyen, Hop D. Nguyen, Pham Hung Quy
We study how the properties of being reduced, integral domain, and normal, behave under small perturbations of the defining equations of a noetherian local ring. It is not hard to…
On the ordinary and symbolic powers of fiber products
Hoang Viet Do, Hop D. Nguyen, Seyed Amin Seyed Fakhari
We completely determine the depth and regularity of symbolic powers of the fiber product of two homogeneous ideals in disjoint sets of variables, given knowledge of the symbolic po…
Asymptotic depth of invariant chains of edge ideals
Tran Quang Hoa, Do Trong Hoang, Dinh Van Le +2
We completely determine the asymptotic depth, equivalently, the asymptotic projective dimension of a chain of edge ideals that is invariant under the action of the monoid Inc of in…
Fiber criteria for flatness and homomorphisms of flat affine group schemes
Phùng Hô Hai, Hop D. Nguyen, João Pedro dos Santos
A very useful result concerning flatness in Algebraic Geometry is EGA's ``fiber'' criterion. We propose similar fiber criteria to verify flatness of a module while avoiding ``finit…