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Contraction criteria
for reducible rational curves with components of length one
in smooth complex threefolds
Tom Zerger |
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Vol. 212 (2003), No. 2, 377–394
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Abstract |
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Let X be a smooth complex threefold and C a linear chain of n smooth rational curves in X, each intersecting the canonical sheaf 𝒦X trivially, and each having length 1, where the length is Kollár’s invariant. Formal criteria will be given to determine when C contracts, when C deforms, and when C neither contracts or deforms in X, the formal completion of X. It is shown precisely, using the curve C, its components, and their defining ideals, how the behavior of C coincides with the deformation theory of the compound An singularity. |
Milestones
Received: 9 September 2002
Published: 1 December 2003
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Authors |
| Tom Zerger | |
| Department of Mathematics Saginaw Valley State University University Center, MI 48710 |
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