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Terminal 3-fold Divisorial Contractions of a Surface to a Curve I

Published online by Cambridge University Press:  04 December 2007

Nikolaos Tziolas
Nikolaos Tziolas
Affiliation:
Department of Mathematics, University of Crete, Knossos Ave., Heraklion 71409, Greece. e-mail: tziolas@math.uch.gr
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Abstract

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Let Γ ⊂ X be a smooth curve on a 3-fold which has only index 1 terminal singularities along Γ. In this paper we investigate the existence of extremal terminal divisorial contractions E ⊂ Y→Γ ⊂ X, contracting an irreducible surface E to Γ. We consider cases with respect to the singularities of the general hypersurface section S of X through Γ. We completely classify the cases when S is Ai, i ≤ 3, and D2n for any n.

Keywords

algebraic geometry
Type
Research Article
Information
Compositio Mathematica , Volume 139 , Issue 3 , December 2003 , pp. 239 - 261
Copyright
© 2003 Kluwer Academic Publishers