Atiyah class and sheaf counting on local Calabi Yau fourfolds

Duiliu Emanuel Diaconescu, Artan Sheshmani, Shing Tung Yau

Research output: Contribution to journalArticlepeer-review

Abstract

We discuss 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. We 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 us to relate our 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]. We finally make predictions about modularity of such fourfold invariants when the base surface is an elliptic K3.

Original languageEnglish (US)
Article number107132
JournalAdvances in Mathematics
Volume368
DOIs
StatePublished - Jul 15 2020
Externally publishedYes

Keywords

  • Calabi-Yau fourfold
  • Donaldson-Thomas invariants
  • Universal Atiyah class

ASJC Scopus subject areas

  • Mathematics(all)

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