an overview of the literature listing Fano fourfolds
Sources that produce an actual enumeration of Fano fourfolds. The count column gives the size the paper claims (its kind, families / cases / deformation classes / new examples, beneath). Constructions differ widely (toric, projective bundles, Grassmannian zero loci, quiver flag zero loci, Cox-ring hypersurfaces, Lefschetz-defect classifications, …), so the shared currency for comparison is the numerical invariants listed in the last column.
| code | reference | year | count | construction |
|---|---|---|---|---|
| SW90a | Szurek, M., & Wiśniewski, J. A. (1990). Fano bundles over P3 and Q₃. Pacific J. Math., 141(1), 197–208. | 1990 | 5 | projective-bundle |
| SSW91 | Sols, I., Szurek, M., & Wiśniewski, J. A. (1991). Rank-2 Fano bundles over a smooth quadric Q₃. Pacific J. Math., 148(1), 153–159. | 1991 | 5 | projective-bundle |
| SW90b | Szurek, M., & Wiśniewski, J. A. (1990). On Fano manifolds, which are Pk-bundles over P2. Nagoya Math. J., 120, 89–101. | 1990 | 12 | projective-bundle |
| Kuc95 | Küchle, O. (1995). On Fano 4-fold of index 1 and homogeneous vector bundles over Grassmannians. Math. Z., 218(4), 563–575. | 1995 | 21 | zero-locus-grassmannian |
| Bat99 | Batyrev, V. V. (1999). On the classification of toric Fano 4-folds. In J. Math. Sci. (New York) (Vol. 94, pp. 1021–1050). | 1999 | 123 | toric |
| CKP15 | Coates, T., Kasprzyk, A., & Prince, T. (2015). Four-dimensional Fano toric complete intersections. Proc. A, 471(2175), 20140704, 14. | 2015 | 738 | ci-toric |
| Ben18 | Benedetti, V. (2018). Manifolds of low dimension with trivial canonical bundle in Grassmannians. Math. Z., 290(1–2), 251–287. | 2018 | – | zero-locus-grassmannian |
| Kal19 | Kalashnikov, E. (2019). Four-dimensional Fano quiver flag zero loci. Proc. A, 475(2225), 20180791, 23. | 2019 | 141 | quiver-flag-zero-locus |
| CGKS20 | Coates, T., Galkin, S., Kasprzyk, A., & Strangeway, A. (2020). Quantum periods for certain four-dimensional Fano manifolds. Exp. Math., 29(2), 183–221. | 2020 | – | mixed |
| HLM22 | Hausen, J., Laface, A., & Mauz, C. (2022). On smooth Fano fourfolds of Picard number two. Rev. Mat. Iberoam., 38(1), 53–93. | 2022 | 67 | cox-ring-hypersurface |
| CRS22 | Casagrande, C., Romano, E. A., & Secci, S. A. (2022). Fano manifolds with Lefschetz defect 3. J. Math. Pures Appl. (9), 163, 625–653. | 2022 | 19 | lefschetz-defect-classification |
| Sec23 | Secci, S. A. (2023). Fano fourfolds having a prime divisor of Picard number 1. Adv. Geom., 23(2), 267–280. | 2023 | 28 | blowup |
| HS23 | Höring, A., & Secci, S. A. (2025). Fano fourfolds with large anticanonical base locus. J. Inst. Math. Jussieu, 24(3), 1021–1051. | 2025 | 22 | anticanonical-base-locus |
| Pas25 | Pastorino, F. (2025). On Casagrande-Druel Fano varieties with Lefschetz defect 2. | 2025 | 147 | casagrande-druel |