# Atiyah class and sheaf counting on local Calabi Yau fourfolds

Artan sheshmani presents new result on arXiv

2018.10.23 | Jane Jamshidi

Artan Sheshmani has submitted a new result on arXiv jointly with Duiliu-Emanuel Diaconescu (Rutgers) & Shing-Tung Yau (Harvard University).

Regarding Donaldson-Thomas (DT) invariants of torsion sheaves with 2 dimensional support on a smooth projective surface in an ambient non-compact Calabi Yau fourfold given by the total space of a rank 2 bundle on the surface, they prove that in certain cases, when the rank 2 bundle is chosen appropriately, the universal truncated Atiyah class of these codimension 2 sheaves reduces to one, defined over the moduli space of such sheaves realized as torsion codimension 1 sheaves in a noncompact divisor (threefold) embedded in the ambient fourfold. Such reduction property of universal Atiyah class enables one to relate ones fourfold DT theory to a reduced DT theory of a threefold and subsequently then to the moduli spaces of sheaves on the base surface using results in [15, 16]. Further they make predictions about modularity of such fourfold invariants when the base surface is an elliptic K3.

Link to the paper on arXiv

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