K-theoretic Donaldson–Thomas theory and the Hilbert scheme of points on a surface
Noah Arbesfeld
Abstract
Integrals of characteristic classes of tautological sheaves on the Hilbert scheme of points on a surface frequently arise in enumerative problems. We use the K-theoretic Donaldson-Thomas theory of certain toric Calabi-Yau threefolds to study K-theoretic variants of such expressions.
Topics & Concepts
Hilbert schemeMathematicsScheme (mathematics)Surface (topology)Hilbert R-treeHilbert spaceHilbert manifoldRigged Hilbert spacePure mathematicsProjective Hilbert spaceAlgebra over a fieldMathematical analysisPoint (geometry)Fixed pointHilbert–Poincaré seriesAlgebraic Geometry and Number TheoryGeometry and complex manifoldsAdvanced Combinatorial Mathematics