5 citations · 8 across the 3 of their papers we have counts for
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Some cases of the Eisenbud-Green-Harris conjecture
Giulio Caviglia, Diane Maclagan
The Eisenbud-Green-Harris conjecture states that a homogeneous ideal in k[x_1,...,x_n] containing a homogeneous regular sequence f_1,...,f_n with deg(f_i)=a_i has the same Hilbert…
The pinched Veronese is Koszul
Giulio Caviglia
In this paper we prove that the coordinate ring of the pinched Veronese (i.e ) is Koszul. The strategy of the proof is…
A Theorem of Eakin and Sathaye and Green's Hyperplane Restriction Theorem
Giulio Caviglia
A Theorem of Eakin and Sathaye relates the number of generators of a certain power of an ideal with the existence of a distinguished reduction for that ideal. We prove how this res…
Bounds on the Castelnuovo-Mumford regularity of tensor products
Giulio Caviglia
In this paper we show how, given a complex of graded modules and knowing some partial Castelnuovo-Mumford regularities for all the modules in the complex and for all the positive h…
Characteristic-free bounds for the Castelnuovo-Mumford regularity
Giulio Caviglia, Enrico Sbarra
We study bounds for the Castelnuovo-Mumford regularity of homogeneous ideals in a polynomial ring in terms of the number of variables and the degree of the generators. In particula…