Research

Papers and Preprints

• A combinatorial characterization of S2 binomial edge ideals (with Antonio Macchia, Giancarlo Rinaldo and Francesco Strazzanti), arXiv version.

• Cohen-Macaulay binomial edge ideals of small graphs (with Antonio Macchia, Giancarlo Rinaldo and Francesco Strazzanti), Journal of Algebra, Vol. 638 (2024) pp. 189-213. 

• Immanant varieties (with Paolo Sentinelli), Linear Algebra and Its Applications, Vol. 682 (2024) pp. 164-190. 

• Linear extensions and shelling orders (with Paolo Sentinelli), Bullettin of the London Mathematical Society, Vol. 55, Issue 6 (2023).

• Cohen-Macaulay binomial edge ideals and accessible graphs (with Antonio Macchia and Francesco Strazzanti), Journal of Algebraic Combinatorics, Vol. 55 (2022). 

• Powers of monomial ideals with characteristic-dependent Betti numbers (with Antonio Macchia, Francesco Strazzanti and Volkmar Welker), Research in the Mathematical Sciences, Vol 9(2), no. 26 (2022).

• P-flag spaces and incidence stratifications (with Paolo Sentinelli), Selecta Mathematica, Vol 27, no. 72 (2021). 

• Non-ridge-chordal complexes whose clique complex has shellable Alexander dual  (with Bruno Benedetti), Journal of Combinatorial Theory, Series A, Vol. 180 (2021).

• Betti splitting from a topological point of view (with Ulderico Fugacci), Journal of Algebra and Its Applications, Vol 19, no. 6 (2020).

• Binomial edge ideals of bipartite graphs (with Antonio Macchia, Francesco Strazzanti), European Journal of Combinatorics, Vol. 70 (2018), pp. 1-25. 

• The poset of proper divisibility (with Antonio Macchia, Emanuele Ventura and Volkmar Welker), SIAM Journal on Discrete Mathematics, Vol. 31 (3), pp. 2093-2109 (2017). 

• Recursive Betti numbers for Cohen-Macaulay d-partite clutters arising from posets, Journal of Pure and Applied Algebra, Vol. 220, Issue 9, pp. 3102-3118 (2016). 

• Betti splitting via componentwise linear ideals, Journal of Algebra, Vol. 455, pp. 1-13 (2016). 

• Cohomological dimension and arithmetical rank of some determinantal ideals (with Alessio Caminata, Antonio Macchia and Maral Mostafazadehfard), Le Matematiche, Vol. 70, Fasc. 1, pp. 273-300 (2015). 

Research interests

The leitmotiv of my research interests plays between Commutative Algebra, Combinatorics and Algebraic Geometry. 

• Minimal graded free resolutions of monomial ideals and Stanley-Reisner theory

• Combinatorial properties of simplicial complexes (shellability, constructibility, vertex-decomposability...)

• Homological invariants of projective varieties

In particular

• Triangulations of topological manifolds

• Matroids and generalizations of the maximality property

• Discrete Morse Theory and related topics (reduction methods for computational homology, collapsibility, non-evasiveness...)

• Binomial edge ideals

• Flag varieties, Grassmannians and their generalizations