9 citations · 56 across the 26 of their papers we have counts for
5 papers · 1 filter
On a conjecture by Kalai
Giulio Caviglia, Alexandru Constantinescu, Matteo Varbaro
We show that monomial ideals generated in degree two satisfy a conjecture by Eisenbud, Green and Harris. In particular we give a partial answer to a conjecture of Kalai by proving…
Betti tables of -Borel-fixed ideals
Giulio Caviglia, Manoj Kummini
In this note we provide a counter-example to a conjecture of K. Pardue [Thesis, Brandeis University, 1994.], which asserts that if a monomial ideal is -Borel-fixed, then its $\n…
Poset Embeddings of Hilbert functions and Betti numbers
Giulio Caviglia, Manoj Kummini
We study inequalities between graded Betti numbers of ideals in a standard graded algebra over a field and their images under embedding maps, defined earlier by us in [Math. Z. 274…
The lex-plus-power inequality for local cohomology modules
Giulio Caviglia, Enrico Sbarra
We prove an inequality between Hilbert functions of local cohomology modules supported in the homogeneous maximal ideal of standard graded algebras over a field, within the framewo…
Koszul property of projections of the Veronese cubic surface
Giulio Caviglia, Aldo Conca
Let V be the Veronese cubic surface in P^9. We classify the projections of V to P^8 whose coordinate rings are Koszul. In particular we obtain a purely theoretical proof of the Kos…