Intersection cohomology of moduli spaces of sheaves on surfaces

2016/12/22 by Jan Manschot, Sergey Mozgovoy · 14 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Algebra over a field #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Cohomology #Combinatorics #Geography #Geometry #Intersection (aeronautics) #Intersection homology #Intersection theory #Mathematical analysis #Mathematics #Moduli #Moduli space #Physics #Pure mathematics #Rank (graph theory) #Surface (topology) #hep-th #math.AG

paper · pdf · doi:10.1007/s00029-018-0431-1

published in Selecta Mathematica 24(5), 3889-3926 (Birkhäuser) · 25 pages

arxiv created 2016/12/22 · openalex publication_date 2018/08/14 · arxiv updated 2019/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We study intersection cohomology of moduli spaces of semistable vector bundles on a complex algebraic surface. Our main result relates intersection Poincare polynomials of the moduli spaces to Donaldson-Thomas invariants of the surface. In support of this result, we compute explicitly intersection Poincare polynomials for sheaves with rank two and three on ruled surfaces.

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