In this paper we prove that if S is a smooth, irreducible, projective, rational, complex surface and D an effective, connected, reduced divisor on S, then the pair (S,D) is contractible (i.e., there is a birational map φ: S →S’ with S’ smooth such that φ∗(D) = 0) if kod(S,D) = −∞. More generally, we even prove that this contraction is possible without blowing up an assigned cluster of points on S. Using the theory of peeling, we are also able to give some information in the case D is not connected.
Contractible curves on a rational surface
Calabri, Alberto
;
2018
Abstract
In this paper we prove that if S is a smooth, irreducible, projective, rational, complex surface and D an effective, connected, reduced divisor on S, then the pair (S,D) is contractible (i.e., there is a birational map φ: S →S’ with S’ smooth such that φ∗(D) = 0) if kod(S,D) = −∞. More generally, we even prove that this contraction is possible without blowing up an assigned cluster of points on S. Using the theory of peeling, we are also able to give some information in the case D is not connected.File in questo prodotto:
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