PIRSA:18110087

K-theoretic Donaldson-Thomas theory and the Hilbert scheme of points on a surface

Arbesfeld, N. (2018). K-theoretic Donaldson-Thomas theory and the Hilbert scheme of points on a surface . Perimeter Institute. https://pirsa.org/18110087

Arbesfeld, Noah. K-theoretic Donaldson-Thomas theory and the Hilbert scheme of points on a surface . Perimeter Institute, Nov. 26, 2018, https://pirsa.org/18110087 

          @misc{ pirsa_PIRSA:18110087,
            doi = {10.48660/18110087},
            url = {https://pirsa.org/18110087},
            author = {Arbesfeld, Noah},
            keywords = {Mathematical physics},
            language = {en},
            title = {K-theoretic Donaldson-Thomas theory and the Hilbert scheme of points on a surface },
            publisher = {Perimeter Institute},
            year = {2018},
            month = {nov},
            note = {PIRSA:18110087 see, \url{https://pirsa.org}}
          }

Noah Arbesfeld Imperial College London

DOI 10.48660/18110087
Collection
Talk Type Scientific Series
Subject

Abstract

Integrals of characteristic classes of tautological sheaves on the Hilbert scheme of points on a surface often arise in enumerative problems. We explain how to use the K-theoretic Donaldson-Thomas theory of toric Calabi-Yau threefolds to study K-theoretic versions of such expressions.

Namely, we explicate a precise relationship between K-theoretic Donaldson-Thomas theory and the refined topological vertex of Iqbal, Kosçaz and Vafa. Applying such results to specific toric threefolds, we deduce dualities satisfied by certain generating series that control integrals over the Hilbert scheme of points on a surface. We then explain how to use these dualities to evaluate certain Euler characteristics of tautological bundles on the Hilbert scheme of points on a general surface.