On the $(-1)$-curve conjecture of Friedman and Morgan

Details On the $(-1)$-curve conjecture of Friedman and Morgan On the $(-1)$-curve conjecture of Friedman and Morgan

1992-09-12

arxiv.org/abs/alg-geom/9209001v2

Mathematics

Algebraic Geometry

13 pages, LaTeX 2.09

Scientific paper

Main difference with previous version: we prove that every differentiably embedded sphere with self intersection $-1$ in a simply connected algebraic surface with $p_g >0$ is homologous to a $(-1)$-curve if $|K_{\min}|$ contains a smooth irreducible curve of genus at least 2 and $p_g$ is even or $K_{\min}^2 \not\equiv 7 \pmod8$ (here $K_{\min}$ is the canonical class of the minimal model).

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