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Families of D ‐Minimal Models and Applications to 3‐Fold Divisorial Contractions
Author(s) -
Tziolas Nikolaos
Publication year - 2005
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/s002461150401514x
Subject(s) - mathematics , divisor (algebraic geometry) , singularity , fold (higher order function) , section (typography) , combinatorics , mathematics subject classification , pure mathematics , geometry , computer science , programming language , operating system
Let X / T be a one parameter family of canonical 3‐folds and let D be a Weil divisor on it flat over T . We study the problem of when the D t ‐minimal models of X t form a family and we obtain conditions for this to happen. As an application of this we classify terminal divisorial contractions E ⊂ Y ← C ⊂ X contracting an irreducible surface E onto the smooth curve C , in the case when the general section of X through C is a D 5 5 DuVal singularity. 2000 Mathematics Subject Classification 14E30 (primary), 14E35 (secondary)