The blowup formula for Donaldson invariants

1994/05/09 by Ronald Fintushel, Ronald J. Stern, Fintushel, Ronald +2
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds #Homotopy and Cohomology in Algebraic Topology #alg-geom #math.AG

paper · pdf · doi:10.48550/arxiv.alg-geom/9405002

16 pages, AMS-LaTeX

openalex publication_date 1994/05/09 · arxiv created 1994/07/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we present a formula which relates the Donaldson invariants of a 4-manifold X with the Donaldson invariants of its blowup X#-CP(2). This blow-up formula is independent of X and involves sigma-functions associated to a naturally arising elliptic function. This, the final version, corrects some earlier misconceptions regarding signs.

Related

• Donaldson invariants of non-simple type 4-manifolds
• Jacobi forms and the structure of Donaldson invariants for 4-manifolds with b₊=1
• Modular forms and Donaldson invariants for 4-manifolds with b₊=1
• Localisation of the Donaldson's invariants along Seiberg-Witten classes
• The Donaldson-Thomas invariants under blowups and flops