Distinguishing embedded curves in rational complex surfaces

Fuller, Terry

doi:10.1090/S0002-9939-98-04001-5

Distinguishing embedded curves in rational complex surfaces
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by Terry Fuller PDF

Proc. Amer. Math. Soc. 126 (1998), 305-310 Request permission

Abstract:

We construct many pairs of smoothly embedded complex curves with the same genus and self-intersection number in the rational complex surfaces $\mathbb {C} P^{2}\# n\overline {\mathbb {C} P}^{2}$ with the property that no self-diffeomorphism of $\mathbb {C} P^{2} \# n \overline {\mathbb {C} P}^{2}$ sends one to the other. In particular, as a special case we answer a question originally posed by R. Gompf (1995) concerning genus two curves of self-intersection number 0 in $\mathbb {C} P^{2} \# 13\overline {\mathbb {C} P}^{2}$.

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