Birational geometry of moduli spaces and special varieties (PRIN 2022 - Project code: 20223B5S8L)
National research project funded by the Italian Ministry of University and Research (PRIN 2022, project code 20223B5S8L), and part of the INABAG – Italian Network for Applied and Birational Algebraic Geometry.
Project data
- Title: Birational geometry of moduli spaces and special varieties
- Funding scheme: PRIN 2022
- Project code: 20223B5S8L
- Host institution: University of Ferrara
- Department: Department of Mathematics and Computer Science
- Project period: 28 September 2023 – 28 February 2026
Scientific aims
The project studies birational and arithmetic properties of moduli spaces and related special varieties, combining techniques from higher dimensional algebraic geometry, the geometry of moduli spaces, and the theory of secant and dual varieties. The research is organised around four main lines:
- Hypersurfaces and quadric bundles. Birational geometry and arithmetic of higher degree hypersurfaces and quadric bundles, with special attention to rationality and unirationality problems.
- Moduli spaces of curves and stable maps. Geometry of moduli spaces of curves and stable maps, including their birational models, effective cones and applications to enumerative geometry.
- Calabi–Yau pairs and the Cremona group. Calabi–Yau pairs and their role in the study of the Cremona group, minimal model program and explicit birational transformations.
- Secant varieties and tensor decompositions. Geometry of secant varieties, identifiability and tensor decomposition algorithms, with applications to applied algebraic geometry.
Principal Investigator
Principal Investigator: Alex Massarenti (University of Ferrara).
Research units
-
Catania – University of Catania
Francesco Russo, Jordi Emanuel Hernández Gómez (postdoc), Giovanni Staglianò, Giuseppe Zappalà. -
Ferrara – University of Ferrara
Alex Massarenti, Philippe Ellia. -
Trento – University of Trento
Elisa Postinghel, Pablo González Mazón (postdoc), Alessandro Oneto, Roberto Pignatelli.
Postdocs supervised by Alex Massarenti
Conferences and workshops organised
Publications supported by the project
- A. Laface, A. Massarenti, W. D. Montoya, Mori dream singular K3 surfaces, preprint 2024, arXiv:2412.17036.
- A. Massarenti, F. Zucconi, The moduli space of genus 8 Fano 3-folds with two ½(1,1,1)-points is rational, preprint 2024, arXiv:2408.13080.
- A. Massarenti, Rational points on even dimensional Fermat cubics, preprint 2024, arXiv:2406.07223.
- M. Bolognesi, A. Massarenti, E. Poma, Cox rings of blow-ups of multiprojective spaces, preprint 2023, arXiv:2308.11283.
- C. Araujo, A. Corti, A. Massarenti, Birational geometry of Calabi–Yau pairs and 3-dimensional Cremona transformations, preprint 2023, arXiv:2306.00207.
- A. Massarenti, M. Mella, Bronowski's conjecture and the identifiability of projective varieties, preprint 2022, arXiv:2210.13524.
- A. Massarenti, M. Mella, On the birational geometry of conic bundles over the projective space, Mathematische Nachrichten 297 (2024), no. 4, 1208–1220, arXiv:2110.10057.
- A. Laface, A. Massarenti, Ample bodies and Terracini loci of projective varieties, Bulletin of the London Mathematical Society 56 (2024), no. 1, 396–410, arXiv:2304.07276.
- A. Massarenti, On the unirationality of quadric bundles, Advances in Mathematics 431 (2023), 109235, arXiv:2204.08793.
- A. Massarenti, Quartic and quintic hypersurfaces with dense rational points, Forum of Mathematics, Sigma 11 (2023), e55, 1–21, arXiv:2212.14626.
- A. Laface, A. Massarenti, R. Rischter, Decomposition algorithms for tensors and polynomials, SIAM Journal on Applied Algebra and Geometry 7 (2023), no. 1, 264–290, arXiv:2107.04097.
- A. Casarotti, E. Corniani, A. Massarenti, Complete singular collineations and quadrics, International Mathematics Research Notices 2023, no. 18, 15370–15407, arXiv:2111.02940.