2019/02/28 by Amin Gholampour, Richard P. Thomas
Mathematics · Physics and Astronomy · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Class (philosophy) #Degeneracy (biology) #Geometry and complex manifolds #Hilbert R-tree #Hilbert scheme #Hilbert space #Projective test #Surface (topology) #Vector bundle #hep-th #math.AG #math.RT #msc:14C05 #msc:14D20 #msc:14J60 #msc:14N35
paper · pdf · doi:10.1112/s0010437x20007290
published as Compositio Math. 156 (2020) 1623-1663 · 42 pages. Two referees' corrections. To appear in Compositio
openalex created_date 2017/10/06 · arxiv created 2020/07/06 · openalex publication_date 2020/08/01 · arxiv updated 2020/10/07 · openalex updated_date 2026/08/05
We express nested Hilbert schemes of points and curves on a smooth projective surface as ‘virtual resolutions’ of degeneracy loci of maps of vector bundles on smooth ambient spaces. We show how to modify the resulting obstruction theories to produce the virtual cycles of Vafa–Witten theory and other sheaf-counting problems. The result is an effective way of calculating invariants (VW, SW, local PT and local DT) via Thom–Porteous-like Chern class formulae.