Family Switching Formula and the $-n$ Exceptional Rational Curves

Details Family Switching Formula and the $-n$ Exceptional Rational Curves Family Switching Formula and the $-n$ Exceptional Rational Curves

2003-08-20

arxiv.org/abs/math/0308197v2

Mathematics

Differential Geometry

59 pages, 1 figure, some name typos fixed

Scientific paper

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 P^1 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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