Chern Classes of Bundles over Rational Surfaces

1997/11/15 by Elizabeth Gasparim, Gasparim, Elizabeth
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #alg-geom #math.AG

paper · pdf · doi:10.48550/arxiv.alg-geom/9711018

A mistake in the original was corrected

openalex publication_date 1997/11/15 · arxiv created 1998/07/27 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Consider the blow up π: \widetildeX → X of a rational surface X at a point. Let \widetildeV be a holomorphic bundle over \widetildeX whose restriction to the exceptional divisor equals \calO(j) ⊕ \cal O(-j) and define V =(π_*\widetildeV)^{\vee \vee}. Friedman and Morgan gave the following bounds for the second Chern classes j ≤ c₂(\widetildeV) - c₂(V) ≤ j². We show that these bounds are sharp.

Citations

• On the topology of holomorphic bundles

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