2 citations · 4 across the 3 of their papers we have counts for
9 papers
The Alexander-Hirschowitz theorem and related problems
Huy Tai Ha, Paolo Mantero
We present a proof of the celebrated result due to Alexander and Hirschowitz which determines when a general set of double points in has the expected Hilbert function…
Betti numbers of Koszul algebras defined by four quadrics
Paolo Mantero, Matthew Mastroeni
Let be an ideal generated by quadrics in a standard graded polynomial ring over a field. A question of Avramov, Conca, and Iyengar asks whether the Betti numbers of $R = S/…
The structure and free resolutions of the symbolic powers of star configurations of hypersurfaces
Paolo Mantero
Star configurations of points are configurations with known (and conjectured) extremal behaviors among all configurations of points in ; additional interest come fro…
Singularities of Rees-like Algebras
Paolo Mantero, Jason McCullough, Lance Edward Miller
Recently, Peeva and the second author constructed irreducible projective varieties with regularity much larger than their degree, yielding counterexamples to the Eisenbud-Goto Conj…
The projective dimension of three cubics is at most 5
Paolo Mantero, Jason McCullough
Let be a polynomial ring over a field and an ideal generated by three forms of degree three. Motivated by Stillman's question, Engheta proved that the projective dimension…
Hypergraphs with high projective dimension and 1-dimensional Hypergraphs
Kuei-Nuan Lin, Paolo Mantero
We prove a sufficient and a necessary condition for a square-free monomial ideal associated to a (dual) hypergraph to have projective dimension equal to the minimal number of g…