3-fold

For the plants known as "threefold", see Trixis. For the chess term, see threefold repetition.

In algebraic geometry, a 3-fold or threefold is a 3-dimensional algebraic variety.

The Mori program showed that 3-folds have minimal models.

References

• Matsuki, Kenji (2002), Introduction to the Mori program, Universitext, Berlin, New York: Springer-Verlag, ISBN 978-0-387-98465-0, MR 1875410
• Reid, Miles (1980), "Canonical 3-folds", Journées de Géometrie Algébrique d'Angers, Juillet 1979/Algebraic Geometry, Angers, 1979, Alphen aan den Rijn: Sijthoff & Noordhoff, pp. 273–310, MR 0605348
• Roth, L. (1955), Algebraic threefolds, with special regard to problems of rationality, Ergebnisse der Mathematik und ihrer Grenzgebiete (N.F.), Heft 6, Berlin, New York: Springer-Verlag, MR 0076426