Blow-up formulas for (-2)-spheres

1994/12/23 by Rogier Brussee, Brussee, Rogier
Mathematics · #Differential Geometry (math.DG) #FOS: Mathematics #dg-ga #math.DG

paper · pdf · doi:10.48550/arxiv.dg-ga/9412004

6 pages, AMS-latex version 1.1

arxiv created 1994/12/23 · arxiv updated 2009/11/30

Abstract

Let X be a simply connected 4-manifold containing a (-1)-sphere e. Fintushel and Stern prove that D_c(exp(te)) = D_c(B(t)) on e^⊥ if c⋅ e is even, D_c(exp(te)) = D_c-e(S(t)) on e^⊥ if c ⋅ e is odd, for some universal series B(t),S(t) ∈ \Q[x][[t]] with x the class of a point. We show that their method can easily be extended to (-2)-spheres τ to give blow up formulas like D_c(exp(tτ)) = D_c(B²(t) + S²(t)/2 τ²) on τ^perp if c⋅ τis even.

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