Donaldson–Thomas invariants of 2-dimensional sheaves inside threefolds and modular forms

Amin Gholampour, Artan Sheshmani

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

Abstract

Motivated by the S-duality conjecture, we study the Donaldson–Thomas invariants of the 2-dimensional Gieseker stable sheaves on a threefold. These sheaves are supported on the fibers of a nonsingular threefold X fibered over a nonsingular curve. In the case where X is a K3 fibration, we express these invariants in terms of the Euler characteristic of the Hilbert scheme of points on the K3 fiber and the Noether–Lefschetz numbers of the fibration. We prove that a certain generating function of these invariants is a vector modular form of weight −3/2 as predicted in S-duality.

Original languageEnglish (US)
Pages (from-to)79-107
Number of pages29
JournalAdvances in Mathematics
Volume326
DOIs
StatePublished - Feb 21 2018
Externally publishedYes

Keywords

  • Donaldson–Thomas invariants
  • Hilbert scheme
  • K3 fibration
  • Modularity
  • Noether–Lefschetz numbers
  • S-duality

ASJC Scopus subject areas

  • Mathematics(all)

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