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Representing nonnegative homology classes of $\mathbb {C}P^2\#n\overline {\mathbb {C}P}{}^2$ by minimal genus smooth embeddings

1999
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Transactions of the American Mathematical Society
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For any nonnegative class ξ in H 2 (CP 2 #nCP 2 , Z), the minimal genus of smoothly embedded surfaces which represent ξ is given for n ≤ 9, and in some cases with n ≥ 10, the minimal genus is also given. For the finiteness of orbits under diffeomorphisms with minimal genus g, we prove that it is true for n ≤ 8 with g ≥ 1 and for n ≤ 9 with g ≥ 2.

doi:10.1090/s0002-9947-99-02422-8
fatcat:oxfskpiagrhtzo5vcece7t3tmi