Rationality of descendent series for Hilbert and Quot schemes of surfaces

• Drew Johnson ^[1] ; Dragos Oprea ^[2] ; Rahul Pandharipande ^[1]
  1. [1] Swiss Federal Institute of Technology in Zurich

     Swiss Federal Institute of Technology in Zurich

     Zürich, Suiza

     
  2. [2] University of California System

     University of California System

     Estados Unidos

     
• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 27, Nº. 2, 2021
• Idioma: inglés
• DOI: 10.1007/s00029-021-00638-1
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• Resumen

  • Quot schemes of quotients of a trivial bundle of arbitrary rank on a nonsingular projective surface X carry perfect obstruction theories and virtual fundamental classes whenever the quotient sheaf has at most 1-dimensional support. The associated generating series of virtual Euler characteristics was conjectured to be a rational function in Oprea and Pandharipande (in, Geom Topol. http://arxiv.org/abs/1903.08787) when X is simply connected. We conjecture here the rationality of more general descendent series with insertions obtained from the Chern characters of the tautological sheaf. We prove the rationality of descendent series in Hilbert scheme cases for all curve classes and in Quot scheme cases when the curve class is 0.