an overview of the literature listing Fano fourfolds
Structural results on extremal and elementary contractions of (Fano) fourfolds. These are not enumerations (they constrain or describe the possible contractions rather than listing varieties), so the count column is omitted. They are the tools behind many of the identifications between entries in the classification lists.
| code | reference | year | construction |
|---|---|---|---|
| Kaw89 | Kawamata, Y. (1989). Small contractions of four-dimensional algebraic manifolds. Math. Ann., 284(4), 595–600. | 1989 | contraction-theory |
| AW96 | Andreatta, M., & Wiśniewski, J. A. (1998). On contractions of smooth varieties. J. Algebraic Geom., 7(2), 253–312. | 1998 | contraction-theory |
| Tak99 | Takagi, H. (1999). Classification of extremal contractions from smooth fourfolds of (3,1)-type. Proc. Amer. Math. Soc., 127(2), 315–321. | 1999 | contraction-theory |
| BCW02 | Bonavero, L., Campana, F., & Wiśniewski, J. A. (2002). Variétés complexes dont l’éclatée en un point est de Fano. C. R. Math. Acad. Sci. Paris, 334(6), 463–468. | 2002 | contraction-theory |
| Tsu10a | Tsukioka, T. (2010). A remark on Fano 4-folds having (3,1)-type extremal contractions. Math. Ann., 348(3), 737–747. | 2010 | contraction-theory |
| Tsu10b | Tsukioka, T. (2010). Fano manifolds obtained by blowing up along curves with maximal Picard number. Manuscripta Math., 132(1–2), 247–255. | 2010 | contraction-theory |
| Fuj14 | Fujita, K. (2014). On a generalization of the Mukai conjecture for Fano fourfolds. Tokyo J. Math., 37(2), 319–333. | 2014 | contraction-theory |
| Ou17 | Ou, W. (2018). Fano varieties with Nef(X)=Psef(X) and ρ(X)=\dim X-1. Manuscripta Math., 157(3–4), 551–587. | 2018 | contraction-theory |