Mathematical Research Letters

Volume 29 (2022)

Number 4

Donaldson–Thomas invariants, linear systems and punctual Hilbert schemes

Pages: 1049 – 1064



Amin Gholampour (Department of Mathematics, University of Maryland, College Park, Md., U.S.A.)

Artan Sheshmani (Dept. of Mathematics and CMSA, Harvard University, Cambridge, Mass., U.S.A.; Institut for Mathematik, Aarhus Universitet, Aarhus, Denmark; and Laboratory of Mirror Symmetry, National Research Univ. Higher School of Economics, Moscow, Russia)


We study certain DT invariants arising from stable coherent sheaves in a nonsingular projective threefold supported on the members of a linear system of a fixed line bundle. When the canonical bundle of the threefold satisfies certain positivity conditions, we relate the DT invariants to Carlsson–Okounkov formulas for the “twisted Euler number” of the punctual Hilbert schemes of nonsingular surfaces, and conclude they have a modular property.

Received 24 January 2020

Accepted 24 December 2020

Published 23 February 2023