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

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Donaldson-Thomas Invariants of 2-Dimensional sheaves inside threefolds and modular forms. / Gholampour, Amin; Sheshmani, Artan.

In: Advances in Mathematics, Vol. 326, 21.02.2018, p. 79-107.

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Gholampour, Amin ; Sheshmani, Artan. / Donaldson-Thomas Invariants of 2-Dimensional sheaves inside threefolds and modular forms. In: Advances in Mathematics. 2018 ; Vol. 326. pp. 79-107.

Bibtex

@article{1a2d507a35ac4d2cbb0086ac013d93a9,
title = "Donaldson-Thomas Invariants of 2-Dimensional sheaves inside threefolds and modular forms",
abstract = "Motivated by the S-duality conjecture, we study the Donaldson-Thomasinvariants of the 2 dimensional Gieseker stable sheaves on a threefold. Thesesheaves are supported on the fibers of a nonsingular threefold X fibered over anonsingular curve. In the case where X is a K3 fibration, we express theseinvariants in terms of the Euler characteristic of the Hilbert scheme of pointson the K3 fiber and the Noether-Lefschetz numbers of the fibration. We provethat a certain generating function of these invariants is a vector modular formof weight -3/2 as predicted in S-duality.",
keywords = "math.AG, hep-th",
author = "Amin Gholampour and Artan Sheshmani",
note = "Minor corrections. 29 pages",
year = "2018",
month = "2",
day = "21",
doi = "10.1016/j.aim.2017.12.015",
language = "English",
volume = "326",
pages = "79--107",
journal = "Advances in Mathematics",
issn = "0001-8708",
publisher = "Academic Press",

}

RIS

TY - JOUR

T1 - Donaldson-Thomas Invariants of 2-Dimensional sheaves inside threefolds and modular forms

AU - Gholampour, Amin

AU - Sheshmani, Artan

N1 - Minor corrections. 29 pages

PY - 2018/2/21

Y1 - 2018/2/21

N2 - Motivated by the S-duality conjecture, we study the Donaldson-Thomasinvariants of the 2 dimensional Gieseker stable sheaves on a threefold. Thesesheaves are supported on the fibers of a nonsingular threefold X fibered over anonsingular curve. In the case where X is a K3 fibration, we express theseinvariants in terms of the Euler characteristic of the Hilbert scheme of pointson the K3 fiber and the Noether-Lefschetz numbers of the fibration. We provethat a certain generating function of these invariants is a vector modular formof weight -3/2 as predicted in S-duality.

AB - Motivated by the S-duality conjecture, we study the Donaldson-Thomasinvariants of the 2 dimensional Gieseker stable sheaves on a threefold. Thesesheaves are supported on the fibers of a nonsingular threefold X fibered over anonsingular curve. In the case where X is a K3 fibration, we express theseinvariants in terms of the Euler characteristic of the Hilbert scheme of pointson the K3 fiber and the Noether-Lefschetz numbers of the fibration. We provethat a certain generating function of these invariants is a vector modular formof weight -3/2 as predicted in S-duality.

KW - math.AG

KW - hep-th

U2 - 10.1016/j.aim.2017.12.015

DO - 10.1016/j.aim.2017.12.015

M3 - Journal article

VL - 326

SP - 79

EP - 107

JO - Advances in Mathematics

JF - Advances in Mathematics

SN - 0001-8708

ER -