9 citations · 56 across the 26 of their papers we have counts for
4 papers · 1 filter
Explicit Stillman bounds for all degrees
Giulio Caviglia, Yihui Liang
In 2016 Ananyan and Hochster proved Stillman's conjecture by showing the existence of a uniform upper bound for the projective dimension of all homogeneous ideals, in polynomial ri…
A Cayley-Bacharach theorem for points in
Giulio Caviglia, Alessandro De Stefani
We prove a Cayley-Bacharach-type theorem for points in projective space that lie on a complete intersection of hypersurfaces. This is made possible by new bounds…
The Eisenbud-Green-Harris conjecture for fast-growing degree sequences
Giulio Caviglia, Alessandro De Stefani
Let be a standard graded polynomial ring over a field, and be a homogeneous ideal that contains a regular sequence of degrees . We prove the Eisenbud-Green-…
Decomposition of local cohomology tables of modules with large E-depth
Giulio Caviglia, Alessandro De Stefani
We introduce the notion of E-depth of graded modules over polynomial rings to measure the depth of certain Ext modules. First, we characterize graded modules over polynomial rings…