Donaldson-Thomas Invariants of 2-Dimensional sheaves inside threefolds and modular forms

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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
JournalAdvances in Mathematics
Pages (from-to)79-107
Number of pages28
StatePublished - 21 Feb 2018

Bibliographical note

Minor corrections. 29 pages

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