Family Switching Formula and the -n Exceptional Rational Curves
Ai-Ko Liu
Abstract
In this paper, we derive the family switching formula of -n two-sphere fiber bundle embedded in a smooth four-manifold fiber bundle. In the smooth category, it is a partial generalization of Fintushel-Stern's argument for four-manifolds. We also derive an algebraic analogue of the family switching formula, allowing the P1 fibration to carry singular fibers. At the end, we apply the idea of switching to compare the canonical algebraic Kuranishi models of different classes on the so-called "universal family".
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