Spin canonical invariants of 4-manifolds and algebraic surfaces

1994/06/13 by Andrei Tyurin, Tyurin, Andrei
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.alg-geom/9406002

openalex publication_date 1994/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 H²(X,\Z) invariant under diffeomorphism; (3) to proving the same result as (2) for surfaces with p_g = 0, in particular the Barlow surface.

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