Papers
Research papers:
Fano 4-folds with b_2>12 are products of surfaces, Inventiones mathematicae 236, 1-16, 2024.
Fano 4-folds with a small contraction, Advances in Mathematics 405, paper no. 108492, 55 pp., 2022.
with Eleonora Romano and Saverio Secci, Fano manifolds with Lefschetz defect 3, Journal de Mathématiques Pures et Appliquées 163, 625-653, 2022. Corrigendum: 168, 108–109, 2022.
with Eleonora Romano, Classification of Fano 4-folds with Lefschetz defect 3 and Picard number 5, Journal of Pure and Applied Algebra 226, paper no. 106864, 13 pp., 2022.
Fano 4-folds with rational fibrations, Algebra & Number Theory 14(3), 787-813, 2020.
with Giulio Codogni and Andrea Fanelli, The blow-up of P^4 at 8 points and its Fano model, via vector bundles on a del Pezzo surface, Revista Matemática Complutense 32, 475-529, 2019.
with Carolina Araujo, On the Fano variety of linear spaces contained in two odd-dimensional quadrics, Geometry & Topology 21, 3009-3045, 2017.
Fano 4-folds, flips, and blow-ups of points, Journal of Algebra 483, 362-414, 2017.
Rank 2 quasiparabolic vector bundles on P^1 and the variety of linear subspaces contained in two odd-dimensional quadrics, Mathematische Zeitschrift 280, 981-988, 2015.
with Stéphane Druel, Locally unsplit families of rational curves of large anticanonical degree on Fano manifolds, International Mathematics Research Notices 2015, 10756-10800, 2015.
On some Fano manifolds admitting a rational fibration, Journal of the London Mathematical Society 90, 1-28, 2014.
Numerical invariants of Fano 4-folds, Mathematische Nachrichten 286, 1107-1113, 2013.
On the birational geometry of Fano 4-folds, Mathematische Annalen 355, 585-628, 2013.
On the Picard number of divisors in Fano manifolds, Annales Scientifiques de l'Ecole Normale Supérieure 45, 363-403, 2012.
On Fano manifolds with a birational contraction sending a divisor to a curve, Michigan Mathematical Journal 58, 783-805, 2009.
Quasi-elementary contractions of Fano manifolds, Compositio Mathematica 144, 1429-1460, 2008.
with Sandra Di Rocco, Projective Q-factorial toric varieties covered by lines, Communications in Contemporary Mathematics 10, 363-389, 2008.
with Priska Jahnke and Ivo Radloff, On the Picard number of almost Fano threefolds with pseudo-index > 1, International Journal of Mathematics 19, 173-191, 2008.
with Lucia Caporaso and Maurizio Cornalba, Moduli of roots of line bundles on curves, Transactions of the American Mathematical Society 359, 3733-3768, 2007.
with Laurent Bonavero and Stéphane Druel, On covering and quasi-unsplit families of curves, Journal of the European Mathematical Society 9, 45-57, 2007.
The number of vertices of a Fano polytope, Annales de l'Institut Fourier 56 (1), 121-130, 2006.
with Edoardo Ballico and Claudio Fontanari, Moduli of Prym curves, Documenta Mathematica 9, 265-281, 2004.
with Lucia Caporaso, Combinatorial properties of stable spin curves, Communications in Algebra 31 (8), 3653-3672, 2003.
Centrally symmetric generators in toric Fano varieties, Manuscripta Mathematica 111, 471-485, 2003.
with Laurent Bonavero, Olivier Debarre, and Stéphane Druel, Sur une conjecture de Mukai, Commentarii Mathematici Helvetici 78, 601-626, 2003.
Toric Fano varieties and birational morphisms, International Mathematics Research Notices 27, 1473-1505, 2003.
Contractible classes in toric varieties, Mathematische Zeitschrift 243, 99-126, 2003.
On the birational geometry of toric Fano 4-folds, Comptes Rendus de l'Académie des Sciences 332, 1093-1098, 2001.
Expository papers:
On some numerical properties of Fano varieties, Bollettino dell'Unione Matematica Italiana 7-B (8), 663-671, 2004. Talk given at the XVII Convegno dell'Unione Matematica Italiana, Milano, 8-13 september 2003.
The Lefschetz defect of Fano varieties, Rendiconti del Circolo Matematico di Palermo Series 2, special issue on Fano varieties 72, 3061-3075, 2023.
Notes:
Mori dream spaces and Fano varieties, expanded notes for a minicourse held at the conference Géométrie Algébrique et Géométrie Complexe, CIRM, Marseille, March 2012.
An informal list of the examples that I know of (smooth, complex) Fano 4-folds with 5 < b_2 < 10. Comments or suggestions of new examples are welcome