References
Danilov, V.: Decomposition of certain birational morphisms. Math. USSR Izv.16, 419–429 (1981)
Frumkin, M.: A filtration in the three-dimensional Cremona group. Math. USSR Sborn.19, 191–208 (1973)
Hironaka, H.: Resolution of singularities of an algebraic variety over a field of characteristic zero. Ann. Math.79, 109–326 (1964)
Hironaka, H.: Flattening theorem in complex-analytic geometry. Am. J. Math.97, 503–547 (1975)
Kulikov, V.: Degenerations ofK3 surfaces and Enriques surfaces. Math. USSR Izv.11, 957–989 (1977)
Kulikov, V.: Decomposition of birational maps of smooth algebraic threefolds modulo codimension two (in Russian). Izv. Akad. Nauk SSSR Ser. Mat.46, 881–895 (1982)
Moishezon, B.: Onn-dimensional compact complex varieties withn algebraically independent meromorphic functions. AMS Transl. Ser. 2,63, 51–177 (1967)
Mumford, D.: The topology of normal singularities of an algebraic surface and a criterion for simplicity. Publ. Math.9, 5–22 (1961)
Persson, U., Pinkham, H.: Degeneration of surfaces with trivial canonical bundle. Ann. Math.113, 45–66 (1981)
van der Waerden, B.: Zur algebraischen Geometrie VI: Algebraische Korrespondenzen und rationale Abbildungen. Math. Ann.110, 134–160 (1934)
Zariski, O.: Reduction of singularities of algebraic three-dimensional varieties. Ann. Math.45, 472–542 (1944)
Author information
Authors and Affiliations
Additional information
Partially supported by NSF Grants MCS 77-18723 (A04) and MCS 8203664
Rights and permissions
About this article
Cite this article
Crauder, B. Two reduction theorems for threefold birational morphisms. Math. Ann. 269, 13–26 (1984). https://doi.org/10.1007/BF01455994
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01455994