The Family Blowup Formula of the Family Seiberg-Witten Invariants

Details The Family Blowup Formula of the Family Seiberg-Witten Invariants The Family Blowup Formula of the Family Seiberg-Witten Invariants

2003-05-20

arxiv.org/abs/math/0305294v1

Mathematics

Differential Geometry

79 pages, supplement of the long paper: family blowup formula, admissible graphs and the enumeration of singular curves, I

Scientific paper

In the paper we formulate and derive the family blowup formula of family Seiberg-Witten invariants. The formula has been used in the enumerative application of counting singular curves on algebraic surfaces. We first give a topological derivation of the formula by using family index theorem. Then we define the algebraic (family) Seiberg-Witten invariants for algebraic surfaces and then give an algebraic derivation of the family blowup formula for the algebraic family Seiberg-Witten invariants.

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