Spin canonical invariants of 4-manifolds and algebraic surfaces

Abstract

The paper is a colloquial-style discussion of invariants of algebraic surfaces analogous to the Donaldson polynomials, arising from moduli spaces of ``jumping'' Yang--Mills instantons, or moduli spaces of jumping vector bundles. The invariants have the following applications: (1) to the Van de Ven conjecture that the Kodaira dimension is a diffeomorphism invariant; (2) to proving that algebraic surfaces with $p_g>0$ have a proper sublattice of $H^2(X,\mathbb{Z})$ invariant under diffeomorphism; (3) to proving the same result as (2) for surfaces with $p_g=0$, in particular the Barlow surface.

amsTeX 2.1 (amsppt format), 23 pages. Also distributed as Warwick preprint 38/1994. Research partly supported by a Royal Society Kapitza fellowship

References in corpus (2)

• Stable pairs on curves and surfaces
• The simple method of distinguishing the underlying differentiable structures of algebraic surfaces

Cited by in corpus (2)

• Localisation of the Donaldson's invariants along Seiberg-Witten classes
• Complete subvarieties in moduli spaces of rank 2 stables sheaves on smooth projective curves and surfaces